Home /
Expert Answers /
Calculus /
a-linear-second-order-differential-equation-is-given-as-y-3y-2y-5ex-10sinx-a-find-the-pa807
(Solved): A linear second-order differential equation is given as y+3y+2y=5ex+10sinx a) Find the ...
![A linear second-order differential equation is given as
\[
y^{\prime \prime}+3 y^{\prime}+2 y=5 e^{-x}+10 \sin x
\]
a) Find t](https://media.cheggcdn.com/media/2e7/2e7e9876-5b2e-4aba-b441-aee3d3e5731f/php1I1FsF)
A linear second-order differential equation is given as a) Find the general solution the corresponding homogeneous differentail equation of the given equation. b) Then find a particular solution of the nonhomogeneous equation by undetermined coefficients. c) Give the general solution of the equation. (Show the details of your work) Note: Your solutions should be written in detail.(including the derivatives and integrals calculations) Method of Undetermined Coefficients
Expert Answer
2) The given differential equation is: a) The corresponding homogeneous equation is: The auxiliary equation is:So the complementary solution (solution of corresponding homogeneous equation) is: where are arbitrary constants