32.8.4 problem Exercise 21.6, page 231

Internal problem ID [5953]
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 21.6, page 231
Date solved : Monday, January 27, 2025 at 01:28:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 32

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

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