15.18.11 problem 11

Internal problem ID [3254]
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
Date solved : Monday, January 27, 2025 at 07:28:51 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{\prime \prime }+x^{\prime } t&=t^{3} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 30

dsolve(diff(x(t),t$2)+t*diff(x(t),t)=t^3,x(t), singsol=all)
 

\[ x = \frac {t^{3}}{3}+\frac {c_{1} \sqrt {\pi }\, \sqrt {2}\, \operatorname {erf}\left (\frac {\sqrt {2}\, t}{2}\right )}{2}-2 t +c_2 \]

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 38

DSolve[D[x[t],{t,2}]+t*D[x[t],t]==t^3,x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \sqrt {\frac {\pi }{2}} c_1 \text {erf}\left (\frac {t}{\sqrt {2}}\right )+\frac {t^3}{3}-2 t+c_2 \]