Differential Equations Answers

Solve the following equations

1. d²y/dx² + 2dy/dx + 2y = e^x sin2x

2. d²y/dx² + 4dy/dx + 4y= x³e^2x

how to solve this x²y''-xy'+y=2x by variation of parameter

how to solve x²y''-3xy'-2y=0

how to solve xy''+y'=0

(y/x^2)+1+1/x dy/dx=0

Solve

solve (3x^2+2xy^2)dx+(2x^2y)dy=0 where y(2)=-3

Consider ODE

(3x^2y^2+x^2)dx+(2x^3y+y^2)dy=0

Find genaral solution

(D2+3D+2)y=cos2x

The function f: R^2~{(x,y)|y=0 or y= 5x} →R

defined by

f(x,y)= x^2-3xy/(y^2+5yx)

is a homogeneous function

True or false with full explanation

Solve the following PDE using the method of separation of variables and Fourier series

u_tt = c²u_xx, 0<x<1, t<0

u(0,t) = 0, t>0

u(1,t) = 0, t>0

u(x,0) = 2x(1-x), 0<=x<=1

u_t(x,0) =0