72.8.29 problem 44

Internal problem ID [14722]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Review Exercises for chapter 1. page 136
Problem number : 44
Date solved : Monday, March 31, 2025 at 12:55:27 PM
CAS classification : [_Abel]

\begin{align*} y^{\prime }&=\left (y-1\right ) \left (y-2\right ) \left (y-{\mathrm e}^{\frac {t}{2}}\right ) \end{align*}

✗ Maple

ode:=diff(y(t),t) = (y(t)-1)*(y(t)-2)*(y(t)-exp(1/2*t)); 
dsolve(ode,y(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[t],t]==(y[t]-1)*(y[t]-2)*(y[t]-Exp[t/2]); 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq((2 - y(t))*(y(t) - 1)*(y(t) - exp(t/2)) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : The given ODE -y(t)**3 + y(t)**2*exp(t/2) + 3*y(t)**2 - 3*y(t)*exp(t/2) - 2*y(t) + 2*exp(t/2) + Derivative(y(t), t) cannot be solved by the factorable group method