Internal problem ID [2255]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial
Solutions. page 529
Problem number: Problem 2.
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-50 \sin \left (3 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)+2*diff(y(x),x)+y(x)=50*sin(3*x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+x \,{\mathrm e}^{-x} c_{1}-4 \sin \left (3 x \right )-3 \cos \left (3 x \right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 31
DSolve[y''[x]+2*y'[x]+y[x]==50*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -4 \sin (3 x)-3 \cos (3 x)+e^{-x} (c_2 x+c_1) \\ \end{align*}