Internal problem ID [12789]
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: 5.
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: 5.437 (sec). Leaf size: 29
dsolve(diff(y(x),x$2)+9*y(x)=2*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\cos \left (3 x \right ) \left (x -3 y \left (0\right )\right )}{3}+\frac {\sin \left (3 x \right ) \left (1+3 D\left (y \right )\left (0\right )\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 33
DSolve[y''[x]+9*y[x]==2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x}{3}+c_1\right ) \cos (3 x)+\frac {1}{18} (1+18 c_2) \sin (3 x) \]