Internal problem ID [11710]
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 (ii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{\prime \prime }-4 x^{\prime }=t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(x(t),t$2)-4*diff(x(t),t)=t^2,x(t), singsol=all)
\[ x \left (t \right ) = -\frac {t^{2}}{16}-\frac {t^{3}}{12}+\frac {c_{1} {\mathrm e}^{4 t}}{4}-\frac {t}{32}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.096 (sec). Leaf size: 36
DSolve[x''[t]-4*x'[t]==t^2,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {1}{96} \left (-8 t^3-6 t^2-3 t+24 c_1 e^{4 t}+96 c_2\right ) \]