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]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y=\sin \left (x \right ) \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=sin(x)*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x}{2}} \sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_{2} +{\mathrm e}^{-\frac {x}{2}} \cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} +\frac {\sin \left (2 x \right )}{13}-\frac {3 \cos \left (2 x \right )}{26}+\frac {15 \cos \left (4 x \right )}{482}-\frac {2 \sin \left (4 x \right )}{241} \]
✓ Solution by Mathematica
Time used: 5.225 (sec). Leaf size: 80
DSolve[y''[x]+y'[x]+y[x]==Sin[x]*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{13} \sin (2 x)-\frac {2}{241} \sin (4 x)-\frac {3}{26} \cos (2 x)+\frac {15}{482} \cos (4 x)+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right ) \]