Find the general solution of d²y x(x +2) dy + (x + 2)y(x) = x³, dx dx? given that y, (x) = x and y2(x) = xe* are linearly independent solutions of the corresponding homogeneous equation. Use variation of parameters.

Q: Solve (y2 + xy) dx - x2 dy = 0.

A: We have to find out the solution of the given differential equation

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…

A:

Q: solve  (y2+2x2y)dx+(2x3-xy)dy=0

A: Consider the given differential equation:

Q: Solve: (xy – 1) dx + (x² - xy) dy = 0 %D |

A:

Q: Solve (5x + 9y) dx + (9x+ 5y) dy

A:

Q: Solve this linear IVP,        xlnx dy/dx + y= 2lnx,                           y(e)=2

A:

Q: Solve 2- (2xy - 2y)dx + (3x'y-4x)dy 0

A: We have to solve given problem:

Q: homogeneous equation

A:

Q: Solve by separating variables (x-4)y dx-x³ (y²-3) dy=0

A:

Q: (2x-2y-1)dx-(x-y+1)dy=0

A:

Q: Eliminate the arbitrary constant. y=Ax 5 + Bx3

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Q: 4. The region bounded by the given curves is rotated about the specified axis. Find the volume of…

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Q: Eliminate the arbitrary constant. y=Ax 5+ Bx³ A B 7xy "- x²y + 15y = 0 D x²y '- 7xy "+15y = 0…

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Q: Solve zx+zzy= 2x, z(0, y) = y

A:

Q: Solve (yz + хуz) dx + (zx + хуz) dy + (ху + хуz) dz =

A:

Q: Solve (3x*y? – x²)dy + (4x³y3 - 2xy)dx 0 %3D | | .3

A: Given differential equation is exact differential equation. We solve it as follows:

Q: Solve (2x – 1)3y" + (2x – 1)y' - 2y = 8x? – 2x + 3 %3D |

A:

Q: Solve y(y ³-x) dx + x(y² + x) dy=0 A B 2xy²-x²=cy² D 3 3 2xy ³ - x²=cy ³ © 2xy³-x²=cy² (C) 2xy³ – x³…

A:

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: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: Solve ÿ + 6ỷ + 9y = 0 dy + 2y = e-4 dx d²y + y = 0 dx2 dx²

A: Note : There are multiple questions. Here is the solution of first question. Given differential…

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

A:

Q: Solve (2xy-2xy- = 0 4xy² +2x) dx + (3x2y + 4y) dy %3D

A:

Q: Solve (x²+y)dx+(y³+x)dy=0

A: Since, the given differential equation is x2+ydx+y3+xdy=0, we have to find the general solution.

Q: Solve (xy+x)dx - (x2y2+x2+y2+1)dy=0 using separation of variable

A: Let's find.

Q: B. Solve DES: (x+y) dx + (3x+3y-4) dy =0 C. Solve DES: y' + y = x/y

A: Given: It is given that the equations are x+ydx+3x+3y-4dy=0 and y'+y=xy. To find: The main objective…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.