Find the general solution of the equation y'' + 4y = e^x\cos 2x

Question:

Find the general solution of the equation {eq}y'' + 4y = e^x\cos 2x {/eq}

Method of Undetermined Coefficients:

Method of undetermined coefficients is a powerful approach to solve wide variety of Linear constant coefficient differential equations with forcing functions involving exponential and trigonometric sines and cosines:

If the forcing function is of the form:

{eq}p(x)=e^{x}\cos(2x) {/eq}

Then the Particular solution is given as:

{eq}y_p(x)=e^x(A\cos(2x)+B\sin(2x)) {/eq}

Answer and Explanation:

Become a Study.com member to unlock this answer! Create your account

View this answer

The given differential equation is:

{eq}(D^2+4D)y=e^x\cos(2x) {/eq}

The complimentary solution is given by roots of:

{eq}D^2+4D=0\\ D_1=0\\ D_2=...

See full answer below.


Learn more about this topic:

Undetermined Coefficients: Method & Examples
Undetermined Coefficients: Method & Examples

from

Chapter 10 / Lesson 15
3.9K

The method of undetermined coefficients is used to solve a class of nonhomogeneous second order differential equations. This method makes use of the characteristic equation of the corresponding homogeneous differential equation.


Related to this Question

Explore our homework questions and answers library