Differential Equations Answers

(d^2-5d+6)y =x cos(2x)

1. y²dx-(xy+y²)dy=0

Let substitution v=y/x ; y=vx ; dy= vdx+xdv

2. x²dy+(2xy-y²)dx=0

Let substitution v=y/x ; y=vx ; dy= vdx+xdv

Determine the form of a particular solution for each differential equation. No need to solve for the general solution of the differential equation.

1. y'' − 3y' + 2y = xe^x + 1

Find the integral surface of the PDE:

x²p + y²q +z² =0

which passes through the hyperbola

xy =x+y, z=1.

Solve (p + q)(px + qy) = 1, using Charpit’s method.

Solve:

x².d²y/dx² -x.dy/dx +y=ln x

(D^4 +13D^2 + 36)y = 0