Find the particular solution of the differential equation y"(x) - y(x) = 1+e^x.


Find the particular solution of the differential equation {eq}y"(x) - y(x) = 1+e^x {/eq}.

Particular Solution :

A particular solution is also satisfy the given Differential Equation. We apply the new method to finding the particular solution of the nonhomogeneous differential equations. To find particular solution we use following property as follows

{eq}\displaystyle \frac{1}{f(D)}e^{bt}= \frac{e^{bt}}{f(b)},\quad f(b)\neq 0\: \: \text{if}\enspace f(b)=0\: \: \text{then}\enspace \displaystyle \frac{1}{f(D)}e^{bt}= \frac{t}{f{}'(D)}e^{bt}\\ \displaystyle D\equiv \frac{\mathrm{d} }{\mathrm{d} t}\\ D^{2}\equiv \frac{\mathrm{d^{2}} }{\mathrm{d} t^{2}} {/eq}

Answer and Explanation:

Become a member to unlock this answer! Create your account

View this answer

Consider the differential equation

{eq}\displaystyle y{}''(x) - y(x) = 1+e^x {/eq}

Rewrite the differential equation as follows


See full answer below.

Learn more about this topic:

First-Order Linear Differential Equations


Chapter 16 / Lesson 3

In this lesson you'll learn how to solve a first-order linear differential equation. We first define what such an equation is, and then we give the algorithm for solving one of that form. Specific examples follow the more general description of the method.

Related to this Question

Explore our homework questions and answers library