32.8.6 problem Exercise 21.8, page 231

Internal problem ID [5955]
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 21.8, page 231
Date solved : Monday, January 27, 2025 at 01:28:18 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }+2 y&=8+6 \,{\mathrm e}^{x}+2 \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve(diff(y(x),x$2)+3*diff(y(x),x)+2*y(x)=8+6*exp(x)+2*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -{\mathrm e}^{-2 x} \left (\left (-4+\frac {3 \cos \left (x \right )}{5}-\frac {\sin \left (x \right )}{5}\right ) {\mathrm e}^{2 x}-c_{2} {\mathrm e}^{x}+c_{1} -{\mathrm e}^{3 x}\right ) \]

✓ Solution by Mathematica

Time used: 0.144 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]+3*D[y[x],x]+2*y[x]==8+6*Exp[x]+2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x+\frac {\sin (x)}{5}-\frac {3 \cos (x)}{5}+c_1 e^{-2 x}+c_2 e^{-x}+4 \]