Internal problem ID [12468]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 5. The Laplace Transform Method. Exercises 5.2, page 248
Problem number: 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-9 y=2 \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-9*y(x)=2*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\sin \left (3 x \right )}{9}+y \left (0\right ) \cosh \left (3 x \right )+\frac {\sinh \left (3 x \right ) \left (1+3 D\left (y \right )\left (0\right )\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 30
DSolve[y''[x]-9*y[x]==2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{9} \sin (3 x)+c_1 e^{3 x}+c_2 e^{-3 x} \]