2. Find the general solution of dy d²y dy + 12- dx - 8y = 21e2 - - dx3 dx2

Q: Find the general solution of d²y dy 4- + 4y = 0 - %3D dx?

A: The given differential equation is d2ydx2-4dydx+4y=0.

Q: 5. Solve d²y dy dx² dx +2 + 5y = sin 2x, given that y(0)=3, y'(0)=0.

A:

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy=0

A: The given differential equation is of Reducible Homogeneous form . We solve it using following way .

Q: Find the general solution to dy/dx= 6-x^2/2y^3

A:

Q: Find general solution of: 2x ( y - x^2) dx + dy = 0

A: Topic:- solution of differential equations

Q: Find the general solution of dy/dx=x-4/x^2-5x+6

A: Explanation of the answer is as follows

Q: I. Find the general solution of the following: 1. dy - 2x²¹ dx y 2. dx = xy dx 3. dy = (6e³x + 1)dx…

A:

Q: Find the general solution of dy/dx= xy-y/x^2-5x+

A: To find the general solution of the below differential equation. dydx=xy−yx2−5x+6

Q: Find the general solution of dx -3 y=2cos3x . dx

A: The given differential equation is. d2ydx2+2dydx-3y =2cos3x This can be written as, D2+2D-3y=2cos3x…

Q: Find the solution of (x² – xy – y²) dx + xydy = 0 -- -

A:

Q: Find the general solution of hp dy + 12- dx² dx 8y = 21e2x | dr3

A: To find the general solution of the given differential equation: d3ydx3−6d2ydx2+12dydx−8y=21e2x

Q: Solve the Bernoulli DE dx - 2xy dy = 6x3y2e-2y^2 dy

A:

Q: 2 Find So (3x2 + 4y³) dy dx.

A: Topic:- double integration

Q: The solution to (2x – 4y – 3)dy = (x- 2y)dx is:

A:

Q: General solution for xy dx + (2x2 + 3y2 - 20) dy = 0

A: General solution for xy dx + (2x2 + 3y2 - 20) dy = 0

Q: Obtain the general solution to the equation. dy 1. y + 2x + 1 dx

A: Given that: dydx=yx+2x+1

Q: What is exact solution for dy/dx =(x2+y2)/(x+y)

A: Given: The given equation is dydx=(x2+y2)x+y

Q: I. Solve for the General or Particula 1. dy dx = 3x+xy² y+x²y

A:

Q: Find the general solution for (d2y)/(dx2) + 10(dx)/(dy)+25y = 0

A: Given differential equation is y"+10y'+25y=0 This is second order homogeneous differential equation.…

Q: Solve the particular solution of (xª + y³)dx – 2x° dy= 0 when x = 2, y = 3. -

A: We can rewrite the given equation as,  (xy+y3)dx = 2x3dy xydx+y3dx = 2x3dy

Q: Find the solution of the initial value problem dy 2 - - 4y + 0, y(1) = 2 dx

A: Given differential equation is −xdydx−4y+2x2=0......1 and y1=2. We have to find the solution of the…

Q: Find the complete solution of the following. dy =  ( 2x3 + 4x ) dx         ;         x = 1 when y =…

A: From the given differential equation: dy=2x3+4xdx Now integrate on the both sides. ∫dy=∫2x3+4xdx So,…

Q: Find the particular solution of (dy/dx) = (5x3 + x2 - 2); y = 1 when x = 0

A: Given: dydx=5x3+x2-2; y=1 when x=0

Q: 9. Obtain the general solution to the equation. (X² +36) dy + xy = 7x, y(0) = 2 dx

A: To obtain: The general solution to the equation X2+36dydX+Xy=7X, y0=2

Q: The general solution of (y-1)dx −2(x+y+1)dy=0 by CL2V is

A:

Q: Find the general solution : (3x + 2y + 4) dx + (3x + 2y - 3) dy = 0

A:

Q: Find the general solution by means of separation of variables if: dy = xy -x dx

A:

Q: Find the particular solution from y(9x-2y)dx-x(6x-y)dy=0  when x=1/3 and y=5/2.

A:

Q: Solve for particular solution. (2x-6y+4)dx + (x-2y-3)dy = 0 ; when x = 1, y = 1

A:

Q: find general Solution of DE. 4xg dx +x'dy +3y°dx +2xydyexd

A: The objective is to find the general solution of differential equation 4xydx+x2dy+3y2dx+2xydy-xdx=0

Q: Solve (1+2.x) dy d²y -6(1+2x)- dy -16y = 8(1 + 2x) with y(0) = 0, y'(0) = 2. dx dx?

A: Given differential equation is: (1+2x)2d2ydx2-6(1+2x)dydx+16y=8(1+2x)2 Given differential equation…

Q: I. Find the general solution of the following: 2 dy = -2x + 3x -2x = 3e dx (x²+5)dx- (2y - 1)dy = 0…

A:

Q: Determine the general solution of (x – 2y) dx + (2x + y) dy = 0.

A:

Q: dy dy = xy + 3x – 3x dx dx

A: The given differential equation is: dydx-x2dydx=xy+3x-3x3Therefore:dydx=xy+3x1-x21-x2

Q: Find the general solution of 6y2 dx - x (2x3 + y) dy = 0

A:

Q: Find the particular solution of  y(y^2 + x^2)dx + x(3x^2 − 5y^2)dy = 0 ; when x = 2 , y = 1

A:

Q: dy/dx = 2x3,    y(0) = 3 y =

A: Given Data:   Solve the differential equation,

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

A: Solution

Q: (ve* +y)dx+(2xye* +1)dy = 0

A:

Q: Find the general solution of (x+2y– 4)dx-(2x+5-y)dy = 0

A:

Q: Find the general solution of (y + 1) dx + (4x – y) dy = 0

A: Since we are given with multiple number of questions and our guideline is solve the first question…

Q: 1. Find the general solution of 3 + = y*(2x*) dx

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: What is the general solution of d^2y/dx^2 -4dy/dx -12y =3e^5x and dy/dx -2y = 4-x?

A:

Q: 4. Find the solution of dy 3y = x. dx

A:

Q: Find the general solution for d²y_2dy +3y = x² 2 dr2 dx

A: We have to solve given differential equation:

Q: find the general solution for: x^2*d^2y/dx^2 + x*dy/dx -y=0

A: SolutionGiven    x2d2ydx2+ xdydx - y = 0Gind the general solution of the given differential equation…

Q: 2Y – x²y² -2. dy dx

A: The given differential equation is: dydx=2yx-x2y2

Q: d²y dx² +6 dy dx +9y = 0

A: The given differential equation is;  d2y/dx2 + 6dy/dx +9y=0

Q: 5) SOLVE dy _ yz %3D x2

A: A differential equation is an equation in x,y and derivatives of y. An ordinary differential…

Q: The solution of (1 – y² )dx + (1 + x² )dy = 0 is: %3D

A: