32.8.3 problem Exercise 21.5, page 231

Internal problem ID [5952]
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
Date solved : Monday, January 27, 2025 at 01:28:12 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&={\mathrm e}^{i x} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=exp(I*x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-x} \left (\left (\frac {1}{10}-\frac {3 i}{10}\right ) {\mathrm e}^{\left (1+i\right ) x}-{\mathrm e}^{-x} c_{1} +c_{2} \right ) \]

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==Exp[I*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (\frac {1}{10}-\frac {3 i}{10}\right ) e^{i x}+c_1 e^{-2 x}+c_2 e^{-x} \]