Q261 1 Verify that μ ( x, y) = y is an integrating factor for (A) y d x ( 2 x 1 y) d y = 0 on any open rectangle that does not intersect the x axis or, equivalently, that (B) y 2 d x ( 2 x y 1) d y = 0 is exact on any such rectangle Verify that ySolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more X y 2 dx 2xy x 21 dy 0 y 1 1Help is appreciated EditFind the particular solution of the differential equation (1 – y^2) (1 log x) dx 2xy dy = 0, given that y = 0 when x = 1 CBSE CBSE (Commerce) Class 12 Question Papers 1786 Textbook Solutions Important Solutions 3417 Question Bank Solutions 153 Concept Notes & Videos 447
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(x^2+y^2)dx-2xy dy=0 integrating factor-The solution of the differential equation (x^2 y^2) dx 2xy dy = 0 isSimple and best practice solution for (x^2y^2)dx(x^22xy)dy=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework If it's not what You are looking for type in the equation solver your own equation and let us solve it Equation SOLVE Solution for (x^2y^2)dx(x^22xy)dy=0
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I got mu(y) = e^y The point of an integrating factor is to turn an inexact differential into an exact one One physical application of this is to turn a path function into a state function in chemistry (such as dividing by T to turn q_"rev", a path function, into S, a state function, entropy) I assume that the second terms include 3y^2, not 3y (it would be odd to not simply write 9y)INTEGRATING FACTOR BY FORMULA a)2y(x 2 y x) dx 2 (x 2 2y) dy = 0 b)(7xy y 2) dx 8y 2 dy = 0 c)x 2 y 3 dx x(x 2 y 2 xy 7) dy = 0 d)(3x 2 y 2) dx 2xy dy = 0 Expert Answer Who are the experts? (𝑥^2−𝑦^2 )𝑑𝑥2𝑥𝑦 𝑑𝑦=0 Step 1 Find 𝑑𝑦/𝑑𝑥 (𝑥^2−𝑦^2 )𝑑𝑥2𝑥𝑦 𝑑𝑦=0 2xy dy = − (𝑥^2−𝑦^2 ) dx 2xy dy = (𝑦^2−𝑥^2 ) dx 𝑑𝑦/𝑑𝑥 = (𝑦^2 − 𝑥^2)/2𝑥𝑦 Step 2 Putting F(x, y) = 𝑑𝑦/𝑑𝑥 and finding F(𝜆x, 𝜆y)
They give you the integrating factor is x 2 , so multiply the whole equation by said factor to get (1y 2 /x 2 )dx (12y/x )dy = 0 Now, check for exactness again, dM/dy = dN/dx (these should be partial derivatives) dM/dy = 2y/x 2 dN/dx = 2y/x 2 Therefore this equation is now exact, and solve it like you would any other exact equationX ( x 2 − 3 y 2 x y) = 0 d x ( x 2 3 y 2 x y) = 0 d x(x2 − 3y2 xy) = 0 d x ( x 2 3 y 2 x y) = 0 d If any individual factor on the left side of the equation is equal to 0 0, the entire expression will be equal to 0 0 x = 0 x = 0 x2 − 3y2 xy = 0 x 2 3 y 2 x y = 0 Set the first factor equal to 0 0 最も好ましい (x y)^2 dx (2xy x^21)dy=0 (xxy^2)dx(1x^2)dy=0 リンクを取得 ;
Click here👆to get an answer to your question ️ An integrating factor for the DE (1 y^2)dx (tan^1y x)dy = 0 isIn Maths, an integrating factor is a function used to solve differential equations It is a function in which an ordinary differential equation can be multiplied to make the function integrable It is usually applied to solve ordinary differential equations Also, we can use this factor within multivariable calculus When multiplied by an integrating factor, an inaccurate differential is made (x^(2)y^(2)) dx 2xy dy = 0 Updated On 1 To keep watching this video solution for FREE, Download our App The integrating factor of the differential equation is Class 12th DIFFERENTIAL EQUATIONS Verify that
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Show that {*(x² y²))1 is an integrating factor of the equation (x² y²) dx 2xy dy = 0 and hence solve the equation Answer Find an integrating factor and solve the following equations (3x2y 2xy y3)dx (x2 y2)dy = 0 Show transcribed image text Solve (x y)dx (x – y) dy = 0 Solve (x – y^2) dx 2xy dy = 0 Solve dy/dx = 4 y^2/1 x^2 Solve (ye^xy – 1/y) dx (xe^xy x/y^2) dy = 0 Solve dy/dx y/x = x^2y^2, x > 0 Solve (x 3x^3sin y) dx x^4 cosy dy = 0 given that the function mu(x, y) = x^1 is an integrating factor Solve 1/x dy/dx – 2y/x^2 = x cosx, x > 0 Solve dy/dx = 1 x^2 y
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Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, historySolve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more (X^2Y^2)DxXydy=0 The term within parentheses is recognizable as the exact differential d(y^2/x) ( ^2 ^2 ^2)/(2 ^2 ) The order and degree of the differential equation are √(d^2y/dx^2) = √(dy/dx 5) respectively Differentiating wrtx / = x / ( ^2 ^2 ^2)/(2 ^2 ) v x / = ( ^2 ^2 ^2 2 ^2 ^2 This make think that probably there are some mistakes in your analytical calculus
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Ex 9 5, 4 Show homogeneous (x2 y2) dx 2xy dy = 0 Solved Dy/dx = X2 2y/x (2x Y)dy = (2y X)dx (1 Exy How do you solve dy/dx = y^2xsqrt(1 x^2) where y=1 when Advertisiment Ex 9 5, 9 Show homogeneous y dx x log (y/x) dy 2x Ex 9 6, 9Transcribed Image Textfrom this Question Consider the equation (y^2 2xy)dx x^2 dy = 0 Show the equation is not exact, but becomes exact if we multiply it by y^2 Use the resulting exact equation to find the general (implicit) solution of the original equationY = 10x, where P(x) = 2 x, Q(x) = 10x Integrating factor IF = e R P(x)dx = e2 R dx x = e2ln x = eln x 2 = x2 Multiply equation x2 dy dx 2xy = 10x3 ie d dx x2 ·y = 10x3 Integrate x2y = 5 2 x4 C ie y = 5 2 x2 C x2 Toc JJ II J I Back Solutions to exercises 18 Particular solution y(1) = 3 ie y(x) = 3 when x = 1 ie 3 = 5 2 ·1 C 1 ie 6 2 = 5 2 C ie C = 1 2 ∴ y = 5 2 x 2
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$M~dx N~dy = 0$ $(x^2 y^2 1)~dx x(x 2y)~dy = 0$ $M = x^2 y^2 1$ $N = x(x 2y) = x^2 2xy$ $\dfrac{\partial M}{\partial y} = 2y$(c) ( y 2 x y 1 ) dx ( x 2 x y 1 ) dy = 0With M = y 2 x y 1 and N = x 2 x y 1, note that ( N x M y) / ( x M y N ) = ( x y ) / ( x ( y 2 x y 1 ) y ( x 2 x y 1 ) ) = ( x y ) / ( x y) = 1 Thus, μ = exp ( ∫ d(xy) ) = e xy is an integrating factor The transformed equation is ( y 2 x y 1 ) e xy dx ( x 2 x y 1 ) e xy dy = 0 For the differential equation `(x^2y^2)dx2xy dy=0`, which of the following are true (A) solution is `x^2y^2=cx` (B) `x^2y^2=cx` `x^2y^2=xc` (D) `y (A) solution is `x^2y^2=cx` (B) `x
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In order to find the Integrating factor, solve the value of =1/x Since the value obtained is purely a function of x, we can conclude that the special integrating factor is = e lnx = x Multiply the special integrating factor with the original equation, x(2y 2 2y4x 2)dx (2xy x) dy=0 (2xy 2 2xy4x 3)dx (2x 2 y x 2) dy=0Dividing the entire equation by ' dx ' gives us(1yx2y) dxdy (xx3) =0dxdy xx3y(1x2) = xx3−1 dxdy x(1x2)y(1x2) = xx3−1 dxdy xy = xx3−1 dxdy yP (x) = Q(x)Hence, I F = e∫ P (x)dx= e∫ x1 dx= elog(x)= x Answer verified by Toppr 67 Views The given differential equation is not exact and I think you can't find the integrating factor by known way and an easier way, rather you can solve it as follows (x2 − y2 − y)dx − (x2 − y2 − x)dy = 0 (x2 − y2)(dx − dy) xdy − ydx = 0 (1 − y2 x2)(dx − dy) xdy − ydx x2 = 0 (1 − y2 x2)(dx − dy) d(y x) = 0
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(x y)^2 dx (2xy x^21)dy=0 (1x^2y^2x^2y^2)^1/2xy dy/dx=0 Feb 14, 17 Here is the equation $$(2xyx^2x^4)\,dx(1x^2)\,dy=0$$ It is not exact since partial derivatives are not equal Any help would be appreciated ordinarydifferentialequations Share Cite $$\frac {1}{1x^2}y = \int \frac {x^2}{1x^2}\\ \frac {1}{1x^2}y = x \arctan x C\\ y = x^3 x (1x^2)\arctan x C(1x^2)$$ Share Cite (3y^22xy)dx (2xyx^2)dy=0 classify the equation linear, nonlinear, separable,exact, homogeneous, or one that requires an integration factor Download PDF PrintThat is a function of only one variable, and solve the given equation 3 ydx − xdy = 0 4 3x2ydx 2x3dy = 0 5 2y3dx 3y2dy = 0 6 (5xy 2y 5)dx 2xdy = 0 7 (xy x 2y 1)dx (x 1)dy = 0 8 (27xy2 8y3)dx (18x2y 12xy2)dy = 0
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113k views asked in Class XII Maths by nikita74 (1,017 points) Find the general solution of y 2 dx (x 2 xyy 2 )dy = 0 differential equations For the differential equation `(x^2y^2)dx2xy dy=0`, which of the following are true (A) solution is `x^2y^2=cx` (B) `x^2y^2=cx` `x^2y^2=xc` (D) `yWe have, \ \left( x^2 3xy y^2 \right) dx x^2 dy = 0\ \ \Rightarrow \frac{dy}{dx} = \frac{x^2 3xy y^2}{x^2}\ This is a Q262 In Exercises find an integrating factor;
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Re write as dx (dx y^2–2ydy)/x^2=0 d(x) d(y^2/x)=0 integrating u get x y^2/x=c is the solution where c is an arbitrary constant is the solutionตัวประกอบเพื่อการอินทิเกรต 2Integrating Factor 2 (y^2)dx((x^2)xy)dy=0http//wwwmathunivercom/p/blogpageClick here👆to get an answer to your question ️ Solve the differential equation (x^2 y^2) dx 2xydy = 0
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asked in Mathematics by Ankitk (741k points) If integrating factor of x (1 – x2)dy (2x2y – y – ax3) dx = 0 is e∫p∙dx, then p is equal to (A) 2x2 – 1 (B) {2x2 – 1}/ {x (1 – x2)} {2x2 – ax3}/ {x (1 – x2) (D) ax3 differential equations jee jee mainsDy Dx 2xy F X Y 0 2, Ex 9 6, 14 Find particular solution (1 x2) dy/dx 2xy, Solve the differential equation dy/dx = (2y x) / (2x y, Ex 9 5, 12 Find particular solution x2 dy (xy y2, *Differential Equation dy/dx=x(y 1)^2 with initialSimple and best practice solution for (x^2y^2)dx(x^22xy)dy=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework If it's not what You are looking for type in the equation solver your own equation and let us solve it Equation SOLVE Solution for (x^2y^2)dx(x^22xy)dy=0
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A Suppose we have M(x,y) dx = N(x,y) dy Then the DE is exact if M_yN_x=0 M = 6xy 3y^22y => M_y = 6x6y2 N= 2(xy) => N_x = 2 M_y N_x != 0 => Not an exact DE So, we seek an Integrating Factor mu(u) such that (muM)_y = (muN)_x So, we compute (M_yN_x)/N = (6x6y2 2)/(2(xy)) = 3 So the Integrating Factor is given by mu(x) = e^(int \ 3 \ dx) \ \ \ \ \ \ \5月 05, 21 Simple and best practice solution for (2xy)dy(x^2y^21)dx=0 equation Check how easy it is, and learn it for the future Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your(2y2 3x) dx 2xy dy = 0 Sometimes we can find an integrating factor µ(x,y) so that the equation obtained by multiplying by µ(x,y) (shown below) is exact µ(x,y)M(x,y) dx µ(x,y)N(x,y) dy = 0 Exact Differential Equations Solving an Exact DE Making a DE Exact Conclusion Using an Integrating Factor In order for our integrating factor to work, we need the following to be exact µ(x,y)M(x
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Experts are tested by Chegg as specialists in their subject area We review their content and use your feedback to keep the quality high Previous question Next questionFind the corresponding particular solution for {eq}\displaystyle (x^2y^2)\ dx 2xy\ dy=0 {/eq} using the integrating factor Using an Integrating Factor The given equation is in the form of (x^22xyy^2)dx(x y)^2 dy= Find the particular solution of the differential equation (3xy y^2)dx (x^2 xy)dy = 0, for x = 1, y = 1 asked Nov 17, 18 in Mathematics by monuk ( x^2y2y^23x64=0 Given DE (2xy3)dx(x^24y)dy=0 Comparing above equation with the standard form of DE MdxNdy=0 we get M=2xy3\implies \frac{\partial M}{\partial y}=2x & N=x^24y\implies
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