Internal problem ID [12218]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A.
Dobrushkin. CRC Press 2015
Section: Chapter 2, First Order Equations. Problems page 149
Problem number: Problem 1(g).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [`y=_G(x,y')`]
\[ \boxed {y^{\prime }-t \ln \left (y^{2 t}\right )=t^{2}} \]
✗ Solution by Maple
dsolve(diff(y(t),t)=t*ln(y(t)^(2*t))+t^2,y(t), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.47 (sec). Leaf size: 43
DSolve[y'[t]==t*Log[y[t]^(2*t)]+t^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [\frac {\operatorname {ExpIntegralEi}\left (\log (\text {$\#$1})+\frac {1}{2}\right )}{2 \sqrt {e}}\&\right ]\left [\frac {t^3}{3}+c_1\right ] \\ y(t)\to \frac {1}{\sqrt {e}} \\ \end{align*}