Internal problem ID [239]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y^{\prime }+y-\sin \relax (x ) \sin \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 62
dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x)*sin(3*x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_{2}+{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1}-\frac {4 \sin \left (2 x \right ) \cos \left (2 x \right )}{241}+\frac {\sin \left (2 x \right )}{13}+\frac {15 \left (\cos ^{2}\left (2 x \right )\right )}{241}-\frac {3 \cos \left (2 x \right )}{26}-\frac {15}{482} \]
✓ Solution by Mathematica
Time used: 2.531 (sec). Leaf size: 75
DSolve[y''[x]+y'[x]+y[x]==Sin[x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{13} \sin (2 x)-\frac {2}{241} \sin (4 x)-\frac {3}{26} \cos (2 x)+\frac {15}{482} \cos (4 x)+e^{-x/2} \left (c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \\ \end{align*}