Internal problem ID [233]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-6 y^{\prime }+13 y-x \,{\mathrm e}^{3 x} \sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 44
dsolve(diff(y(x),x$2)-6*diff(y(x),x)+13*y(x)=x*exp(3*x)*sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{3 x} \sin \left (2 x \right ) c_{2}+{\mathrm e}^{3 x} \cos \left (2 x \right ) c_{1}+\frac {x \,{\mathrm e}^{3 x} \left (-2 x \cos \left (2 x \right )+\sin \left (2 x \right )\right )}{16} \]
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 43
DSolve[y''[x]-6*y'[x]+13*y[x]==x*Exp[3*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{64} e^{3 x} \left (\left (-8 x^2+1+64 c_2\right ) \cos (2 x)+4 (x+16 c_1) \sin (2 x)\right ) \\ \end{align*}