Internal problem ID [4645]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 25. Second order differential equations. Further problems 25. page 1094
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-9 y-{\mathrm e}^{3 x}-\sin \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-9*y(x)=exp(3*x)+sin(x),y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-3 x} c_{2}+c_{1} {\mathrm e}^{3 x}-\frac {{\mathrm e}^{3 x}}{36}-\frac {\sin \relax (x )}{10}+\frac {{\mathrm e}^{3 x} x}{6} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 37
DSolve[y''[x]-9*y[x]==Exp[3*x]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sin (x)}{10}+e^{3 x} \left (\frac {x}{6}-\frac {1}{36}+c_1\right )+c_2 e^{-3 x} \\ \end{align*}