Internal problem ID [11515]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.5 Higher order equations. Exercises
page 130
Problem number: 1(e).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {x^{\prime \prime \prime }+x^{\prime \prime }=2 \,{\mathrm e}^{t}+3 t^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(x(t),t$3)+diff(x(t),t$2)=2*exp(t)+3*t^2,x(t), singsol=all)
\[ x \left (t \right ) = \frac {t^{4}}{4}+3 t^{2}-t^{3}+{\mathrm e}^{-t} c_{1} +{\mathrm e}^{t}+t c_{2} +c_{3} \]
✓ Solution by Mathematica
Time used: 0.308 (sec). Leaf size: 40
DSolve[x'''[t]+x''[t]==2*Exp[t]+3*t^2,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \frac {t^4}{4}-t^3+3 t^2+e^t+c_3 t+c_1 e^{-t}+c_2 \]