# 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:

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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

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Chapter 10 / Lesson 15
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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.