90.5.22 problem 23

Internal problem ID [25141]
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 71
Problem number : 23
Date solved : Thursday, October 02, 2025 at 11:53:53 PM
CAS classification : [_rational, _Bernoulli]

\begin{align*} 2 y y^{\prime }&=y^{2}+t -1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

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

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

✓ Mathematica. Time used: 2.339 (sec). Leaf size: 39

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

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

✓ Sympy. Time used: 0.278 (sec). Leaf size: 26

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

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