90.3.22 problem 22

Internal problem ID [25086]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 41
Problem number : 22
Date solved : Thursday, October 02, 2025 at 11:49:44 PM
CAS classification : [_separable]

\begin{align*} 2 y y^{\prime }&={\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 21

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

\begin{align*} y &= \sqrt {{\mathrm e}^{t}+c_1} \\ y &= -\sqrt {{\mathrm e}^{t}+c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.388 (sec). Leaf size: 35

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

\begin{align*} y(t)&\to -\sqrt {e^t+2 c_1}\\ y(t)&\to \sqrt {e^t+2 c_1} \end{align*}

✓ Sympy. Time used: 0.207 (sec). Leaf size: 22

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

\[ \left [ y{\left (t \right )} = - \sqrt {C_{1} + e^{t}}, \ y{\left (t \right )} = \sqrt {C_{1} + e^{t}}\right ] \]