# Solve the differential equation or initial value problem using the method for undetermined constants and variation of parameters.

Solve the differential equation using the method of variation of parameters.

Solve the differential equation or initial-value problem using the method for undetermined constants.

y''-4y=e^x cosx y(0)=1, y'(0)=2

y''+y'- 2y=x - sin 2x y(0)=1, y'(0)=0

y'' + y = cot x 0<x<pi/2

See attached file for full problem description.

https://brainmass.com/math/calculus-and-analysis/initial-value-problem-method-undetermined-constant-105640

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

Solve the differential equation or initial-value problem using the method for undetermined constants

8.

(1) First the solution to the homogeneous differential equation

.

Its characteristic equation has 2 real roots, which are . So the solution is

(2) the particular equation to the differential equation

Assume it has the particular solution has the form of

Plug into the ...

#### Solution Summary

ODEs and IVPs are solved. The solution is detailed and well presented.