Internal problem ID [10487]
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]]
\[ \boxed {x^{\prime \prime \prime }+x^{\prime \prime }-2 \,{\mathrm e}^{t}-3 t^{2}=0} \]
✓ 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: 0.19 (sec). Leaf size: 37
DSolve[x'''[t]+x''[t]==2*Exp[t]+3*t^2,x[t],t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} ((t-4) t+12) t^2+e^t+c_3 t+c_1 e^{-t}+c_2 \\ \end{align*}