Internal problem ID [6390]
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]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }-y=\sin \left (x \right ) {\mathrm e}^{x} x} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 44
dsolve(diff(y(x),x$2)+2*diff(y(x),x)-y(x)=x*exp(x)*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\left (1+\sqrt {2}\right ) x} c_{1} +{\mathrm e}^{\left (\sqrt {2}-1\right ) x} c_{2} -\frac {4 \,{\mathrm e}^{x} \left (\left (x -\frac {31}{34}\right ) \cos \left (x \right )-\frac {\sin \left (x \right ) \left (x +\frac {44}{17}\right )}{4}\right )}{17} \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 59
DSolve[y''[x]+2*y'[x]-y[x]==x*Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-\left (\left (1+\sqrt {2}\right ) x\right )}+c_2 e^{\left (\sqrt {2}-1\right ) x}+\frac {1}{289} e^x ((17 x+44) \sin (x)+(62-68 x) \cos (x)) \]