Internal problem ID [10838]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+9 x-t \sin \left (3 t \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(x(t),t$2)+9*x(t)=t*sin(3*t),x(t), singsol=all)
\[ x \left (t \right ) = c_{2} \sin \left (3 t \right )+\cos \left (3 t \right ) c_{1} +\frac {t \sin \left (3 t \right )}{36}-\frac {\cos \left (3 t \right ) t^{2}}{12} \]
✓ Solution by Mathematica
Time used: 0.069 (sec). Leaf size: 38
DSolve[x''[t]+9*x[t]==t*Sin[3*t],x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \left (-\frac {t^2}{12}+\frac {1}{216}+c_1\right ) \cos (3 t)+\frac {1}{36} (t+36 c_2) \sin (3 t) \\ \end{align*}