Internal problem ID [2283]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x^{\prime \prime }+x^{\prime } t=t^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(x(t),t$2)+t*diff(x(t),t)=t^3,x(t), singsol=all)
\[ x \left (t \right ) = \frac {t^{3}}{3}+\frac {c_{1} \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, t}{2}\right )}{2}-2 t +c_{2} \]
✓ Solution by Mathematica
Time used: 0.108 (sec). Leaf size: 38
DSolve[x''[t]+t*x'[t]==t^3,x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \sqrt {\frac {\pi }{2}} c_1 \text {erf}\left (\frac {t}{\sqrt {2}}\right )+\frac {t^3}{3}-2 t+c_2 \]