Internal problem ID [4103]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 y^{\prime }+2 y-8-6 \,{\mathrm e}^{x}-2 \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
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)
\[ y \relax (x ) = -c_{1} {\mathrm e}^{-2 x}+4+{\mathrm e}^{x}-\frac {3 \cos \relax (x )}{5}+\frac {\sin \relax (x )}{5}+c_{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.064 (sec). Leaf size: 38
DSolve[y''[x]+3*y'[x]+2*y[x]==8+6*Exp[x]+2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x+\frac {\sin (x)}{5}-\frac {3 \cos (x)}{5}+c_1 e^{-2 x}+c_2 e^{-x}+4 \\ \end{align*}