Internal problem ID [12029]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 14, Inhomogeneous second order linear equations. Exercises page
140
Problem number: 14.1 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{\prime \prime }-4 x=t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(x(t),t$2)-4*x(t)=t^2,x(t), singsol=all)
\[ x \left (t \right ) = c_{2} {\mathrm e}^{2 t}+{\mathrm e}^{-2 t} c_{1} -\frac {t^{2}}{4}-\frac {1}{8} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 32
DSolve[x''[t]-4*x[t]==t^2,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\frac {t^2}{4}+c_1 e^{2 t}+c_2 e^{-2 t}-\frac {1}{8} \]