Solve the initial value problem dy y = 5e" + 28e5* dx with y(0) = 8.

Q: Solve y" +5y' = (2x+1)e" -5x

A:

Q: dy 3y Vx +1+x = 0, y(0) =1 dx

A: Explained below

Q: Find d2y/dx2 if e^y− y = x. Write your final answer in terms of x and/or y, and simplify.

A:

Q: Solve (1+x)dy-ydx=0

A:

Q: Solve y'' − 4y' + 4y = 3e2t

A: Solve y'' − 4y' + 4y = 3e2t

Q: Solve dx+ dy 0

A:

Q: dx² dx 543-5+ y = 0; y(0) = 4y'(0) = 0

A: To solv the following initial value problem.

Q: TV Cos X 4-3 Sin x dx 2. Calculate

A: Solution

Q: Solve for y. y' = 7x + xy​; y = - 4 when x = 0

A: Given,  y'=7x+xy,  y=-4 when x=0

Q: Solve ry + (2r* – 1)y = 4x*e %3D

A: Solving the first order differential equation

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.