Question

solve x^{2}y’’ - 7xy’ + 15y = 4x^{6} using
variation of parameter

Answer #1

Solve: x2y’’ - 7xy’ + 15y = 4x6

solve IVP, using variation of parameters
x2y'' - 5xy' + 8y = 32x6
y(1) = 0, y'(1) = -8

find the complete general solution
x2y''−7xy'+16y = x4

Solve the linear system below by using row reduction
3x+15y+34z=-2
4x+21y+47z=-1
3x+15y+33z=-4
has the solution
x= , y= , z=

use
variation of parameter solve DE y"+y'-y=x initial conditions y(0)=0
y'(0)=0

Solve the ODE using Variation of constants
? ′′ − ? = ?−1 − 2?−3

Solve the ODE and show the details:
x3y"'+x2y"-2xy'+2y=x3lnx

For each of the following equations, find the general solution
(perferably using imaginary numbers):
y′′ −2y′ −3y=3e2t;
y′′ +2y′ =3+sin(2t);
x2y′′ +7xy′ +5y=x;
x2y′′ +xy′ +4y=sin(lnx)+sin(2lnx);
y′′ +y=tcost.

Solve the given initial-value problem.
y''' + 3y'' − 13y' − 15y = 0, y(0) =
y'(0) = 0, y''(0) = 1

Solve y’’ – 11y’ + 24y = ex +3x using:
Reduction of order
V.C superposition
Variation of parameters

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