10. y(2x3 -x?y + y³)dx - x(2x³ + y³ )dy = 0

Q: au au = xt at (x > 0,t > 0) ax u(0, t) = 0 u(x,0) = 0

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Q: y" +9y' = 9 tan 3x

A: The solution is given by using method of variation of parameters as follows

Q: Solve the Ricatti differential equation Use As a particular solution

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Q: 1. By applying the method of undetermined coefficients, find the general solution of the following…

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Q: 12. (4х + Зу — 7)dx + (3х — 7у + 4)dy %3D 0; whe х %3D 1,у %3D1

A: Solve for the differential equation (4x+3y-7) dx + (3x-7y+4)dy=0; when x=1,y=1.

Q: xdy − ydx + x³dx = 0

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Q: 9. (x + x* + 2x²y² + y4)dx +y dy = 0; when x = 1,y = 1

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Q: 3y"-Gy'+6y by = = e sec x

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Q: 10. (2ху*eУ + 2хуз + у) dх + (x?y*eУ — х?у?— 3х) dy — 0; when x - -1, у — 1

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Q: Solve the homogenious differential equation Cy²+4y+4y=0; ylo)=1, y'(0) = 3 2 2 ⑤[ +² D² + 5 + D…

A: The homogeneous  differential equation is:The aim is to solve the homogeneous differential equation.

Q: (xy + y ln y)dx + (xy + x In x)dy = 0; when x = 1, y = 1

A: 7. The given differential equation is  (xy + y ln(y))  dx + (xy + x ln(x )) dy= 0   ....(1) with…

Q: 6. (y cos x + 2xev)dx + (sin x + x²e° + 2)dy = 0; when x = 0, y = 0

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Q: (x² + 2xy- 4y?)dx- (x² – 8xy– 4y²)dy=0 | O x² + 4y² = C(x + y) O x2 +y2 = C(x+ 4y) O x2 + 2y? = C(x…

A: Solution(x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0dydx=x2+2xy-4y2x2-8xy-4y2(∙)this differential equation is…

Q: бу" - 7у - 5у %3D2x3 + е-* - 5

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Q: Which differential equation follows the form y'+p(x)y=q(x)? A (В E dy dx dy 4-+y=6x dx - 3xy=4y² dx…

A: I am attaching image so that you understand each and every step.

Q: Solve the differential equation. Indicate the type of differential equation

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Q: 5. (e* – sin y)dx + cos y dy = 0; when x 0,y = 1/2

A: First we will convert the given differential equation into linear differential equation by…