Obtain the general solution of the following equations:   1.) y(y3-x)dx+x(y3+x)dy=0

Q: Solve: (3x – 2xy+ 3y)dx = 4rydy (y +3x)(y – x)3 = Ca³ %3D O (y + 3x) (y – x) = Ca³ (y – 3x)(y + x)3…

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Q: solve  (y2+2x2y)dx+(2x3-xy)dy=0

A: Consider the given differential equation:

Q: Solve the following IVP: (x²y+y +5x2 +5)Y =y2 +y-2; y(1)=2 dy dx

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Q: Consider the equation (34)x = (3y)s where x and y are unknown. The number of possible solutions is

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Q: + y²(x+ 1)² = C

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Q: Solve, (2x+3y-2)dx+(3x-4y+1)dy = 0 %3D

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Q: Obtain the general solution of the following equations:    2y(x2-y+x)dx-(x2-2y)dy=0

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Q: Obtain the general solution of the following equations:   (x-4y-9)dx-(4x+y-2)dy=0

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Q: B) Solve (3x? + 3x y²)dx + (3x²y – 3y² + 2y)dy = 0 %3D

A: First test for exactness:  ∂∂y3x2+3xy2=6xy ∂∂x3x2y-3y2+2y=6xy Since, ∂∂x3x2y-3y2+2y=∂∂y3x2+3xy2 so…

Q: S,(2x-y)dxdydz

A: Consider the integral: ∫12∫0z2∫0y-z2x-ydxdydz

Q: Solve for A y and dy if y = f (x) = -3x + 2x2 – 3x +5 %3D and

A: Given that: y=f(x)  =-3x3+2x2-3x+5

Q: Find the general solution to the equation y4) – 6y" + 9y" = 0. NOTE: Use c1, c2, C3, and c, as…

A: We can rewrite the given equation as y''(y''-6y'+9y)=0 Put y = erx then y' = rerx and y'' = r2erx

Q: Solve the following first order equations: (a) (x²y² + 1)dr + 2r²dy = 0, use the substitution ry =…

A: We have to solve 1st order differential equation using substitution xy = u.

Q: Solve: (3x? – 2xy+ 3y² )dx = 4xydy O (y – 3x) (y + x) = Ca³ O (y + 3x)³(y – x) = Ca³ O (y – 3x)(y +…

A: Proceed as shown below

Q: 2. Solve (y + x²y) dy dr = 1

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Q: . Solve the first order equation (3z²y + 2ry)dx + (x³ + x² + 2y)dy = 0.

A: Solution

Q: Solve for y. x= (3y+5)/(7y-1)

A: To solve for .

Q: 2y Solve (3x²+2) dx + (2x - 4y) dy=0 e A B 2 2y x+xe D xe ²y = 2y² = C r3+xe ³y – 2y³ = C 3y © x³ +…

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Q: solve (x? + y) dx + (y³ + x) dy = 0. A yª + x + B + x + y + (c) = C ,3 3/7 3/4

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Q: he following equations a 02 - 4D + 13)y = y"-4y' %3D 04 6D3 + 13D2 - 12D+

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Q: Find all solutions to the equation (D² – 3D + 2)y(x) = 2e³".

A: Given differential equation is (D2 - 3D + 2)y(x) = 2e3x