90.7.20 problem 20

Internal problem ID [25174]
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 99
Problem number : 20
Date solved : Thursday, October 02, 2025 at 11:57:33 PM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 18

ode:=diff(y(t),t) = y(t)^2; 
ic:=[y(t__0) = y__0]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -\frac {y_{0}}{-1+\left (t -t_{0} \right ) y_{0}} \]

✓ Mathematica. Time used: 0.068 (sec). Leaf size: 18

ode=D[y[t],t]== y[t]^2; 
ic={y[t0]==y0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {\text {y0}}{-t \text {y0}+\text {t0} \text {y0}+1} \end{align*}

✓ Sympy. Time used: 0.081 (sec). Leaf size: 15

from sympy import * 
t = symbols("t") 
t0 = symbols("t0") 
y0 = symbols("y0") 
y = Function("y") 
ode = Eq(-y(t)**2 + Derivative(y(t), t),0) 
ics = {y(t0): y0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {1}{t + \frac {- t_{0} y_{0} - 1}{y_{0}}} \]