Internal problem ID [5637]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Problems for Review and Discovery. Drill excercises. Page 105
Problem number: 3(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+2 y^{\prime }-y-x \,{\mathrm e}^{x} \sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 49
dsolve(diff(y(x),x$2)+2*diff(y(x),x)-y(x)=x*exp(x)*sin(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{\left (\sqrt {2}-1\right ) x} c_{2}+{\mathrm e}^{-\left (1+\sqrt {2}\right ) x} c_{1}+\frac {{\mathrm e}^{x} \left (17 \sin \relax (x ) x -68 x \cos \relax (x )+44 \sin \relax (x )+62 \cos \relax (x )\right )}{289} \]
✓ Solution by Mathematica
Time used: 0.317 (sec). Leaf size: 59
DSolve[y''[x]+2*y'[x]-y[x]==x*Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{289} e^x ((17 x+44) \sin (x)+(62-68 x) \cos (x))+e^{-\left (\left (1+\sqrt {2}\right ) x\right )} \left (c_2 e^{2 \sqrt {2} x}+c_1\right ) \\ \end{align*}