Internal problem ID [4100]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 21. Undetermined
Coefficients
Problem number: Exercise 21.5, page 231.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-{\mathrm e}^{i x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(I*x),y(x), singsol=all)
\[ y \relax (x ) = \left (-{\mathrm e}^{-x} c_{1}+\left (\frac {1}{10}-\frac {3 i}{10}\right ) {\mathrm e}^{i x +x}+c_{2}\right ) {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 37
DSolve[y''[x]+3*y'[x]+2*y[x]==Exp[I*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (\frac {1}{10}-\frac {3 i}{10}\right ) e^{i x}+c_1 e^{-2 x}+c_2 e^{-x} \\ \end{align*}