67.1.7 problem Problem 1(g)

Internal problem ID [13954]
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)
Date solved : Tuesday, January 28, 2025 at 06:09:36 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=t \ln \left (y^{2 t}\right )+t^{2} \end{align*}

✗ 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: 0.286 (sec). Leaf size: 43

DSolve[D[y[t],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*}