68.6.34 problem 35

Internal problem ID [17344]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number : 35
Date solved : Saturday, October 04, 2025 at 05:34:06 PM
CAS classification : [_exact]

\begin{align*} {\mathrm e}^{y}-2 y t +\left (t \,{\mathrm e}^{y}-t^{2}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✗ Maple

ode:=exp(y(t))-2*t*y(t)+(t*exp(y(t))-t^2)*diff(y(t),t) = 0; 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(Exp[y[t]]-2*t*y[t])+(t*Exp[y[t]]-t^2)*D[y[t],t]==0; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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✗ Sympy

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

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