7.5.8 problem 11

Internal problem ID [2354]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.10. Page 80
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 05:34:24 AM
CAS classification : [_Abel]

\begin{align*} y^{\prime }&=y^{3}+{\mathrm e}^{-5 t} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&={\frac {2}{5}} \\ \end{align*}

✗ Maple

ode:=diff(y(t),t) = y(t)^3+exp(-5*t); 
ic:=[y(0) = 2/5]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],t]== y[t]^3+Exp[-5*t]; 
ic={y[0]==4/10}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)**3 + Derivative(y(t), t) - exp(-5*t),0) 
ics = {y(0): 2/5} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -y(t)**3 + Derivative(y(t), t) - exp(-5*t) cannot be solved by the lie group method