Differential Equations Answers

(D²-2DD'+D'²)z=cosy-xsiny

Using the Frobenius method, solve the following ODE:

x²y"+4xy'+(x²+2)y=0

Solve (D^2 -4D+3)y = e^x cos 2x + cos3x 

Given dy/dx=y²/25 and y = 5 when x = 0 Find x when y =2

Solve:(𝐷2 −2𝐷𝐷′ +𝐷′2)𝑍=𝑥2𝑦2𝑒𝑥+𝑦

Y"+6y'+9y=-xe^4x by variation of parameters

For any X and suitable p and q, solve y=Xp^qz for z

*** Y=Xp^q to the power z

Solve the following equation of first order but not of first degree y=2xp-p²

Solve dx/x(x+y) = dy/-y(x+y) = dz/-(x-y)(2x+2y+z)

 Solve the equation of the Linear Homogeneous Differential Equations with Constant 

Coefficients.

1. Solve y’’ – y’ – 2y = 0

2. Solve y’’ + 4y = 0

3. (D3 + 3D2 – 4D)y = 0

4. (D2 – 6D + 9)y = 0