67.1.7 problem Problem 1(g)

Internal problem ID [13883]
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 : Monday, March 31, 2025 at 08:16:13 AM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

ode:=diff(y(t),t) = t*ln(y(t)^(2*t))+t^2; 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✓ Mathematica. Time used: 0.286 (sec). Leaf size: 43

ode=D[y[t],t]==t*Log[y[t]^(2*t)]+t^2; 
ic={}; 
DSolve[{ode,ic},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*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2 - t*log(y(t)**(2*t)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -t*(t + log(y(t)**(2*t))) + Derivative(y(t), t) cannot be solved by the factorable group method