69.1.102 problem 149

Internal problem ID [14255]
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
Date solved : Tuesday, January 28, 2025 at 06:23:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} s^{\prime \prime }-a^{2} s&=1+t \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 32

dsolve(diff(s(t),t$2)-a^2*s(t)=t+1,s(t), singsol=all)
 

\[ s = \frac {{\mathrm e}^{a t} c_{2} a^{2}+{\mathrm e}^{-a t} c_{1} a^{2}-t -1}{a^{2}} \]

✓ Solution by Mathematica

Time used: 0.019 (sec). Leaf size: 31

DSolve[D[s[t],{t,2}]-a^2*s[t]==1+t,s[t],t,IncludeSingularSolutions -> True]
 

\[ s(t)\to -\frac {t+1}{a^2}+c_1 e^{a t}+c_2 e^{-a t} \]