Internal problem ID [12199]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 149.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {s^{\prime \prime }-a^{2} s=t +1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(s(t),t$2)-a^2*s(t)=t+1,s(t), singsol=all)
\[ s \left (t \right ) = {\mathrm e}^{a t} c_{2} +{\mathrm e}^{-a t} c_{1} +\frac {-t -1}{a^{2}} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 31
DSolve[s''[t]-a^2*s[t]==1+t,s[t],t,IncludeSingularSolutions -> True]
\[ s(t)\to -\frac {t+1}{a^2}+c_1 e^{a t}+c_2 e^{-a t} \]