Internal problem ID [5153]
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]]
\[ \boxed {y^{\prime \prime }-9 y={\mathrm e}^{3 x}+\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)-9*y(x)=exp(3*x)+sin(x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-3 x} c_{2} +c_{1} {\mathrm e}^{3 x}+\frac {\left (-1+6 x \right ) {\mathrm e}^{3 x}}{36}-\frac {\sin \left (x \right )}{10} \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 37
DSolve[y''[x]-9*y[x]==Exp[3*x]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {\sin (x)}{10}+e^{3 x} \left (\frac {x}{6}-\frac {1}{36}+c_1\right )+c_2 e^{-3 x} \]