90.5.15 problem 15

Internal problem ID [25134]
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 : 15
Date solved : Thursday, October 02, 2025 at 11:53:39 PM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.042 (sec). Leaf size: 18

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

\[ y = -\sqrt {3 \,{\mathrm e}^{-t^{2}}+1} \]

✓ Mathematica. Time used: 1.781 (sec). Leaf size: 22

ode=y[t]*D[y[t],{t,1}] +t*y[t]^2 == t; 
ic={y[0]==-2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -\sqrt {3 e^{-t^2}+1} \end{align*}

✓ Sympy. Time used: 0.388 (sec). Leaf size: 15

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

\[ y{\left (t \right )} = - \sqrt {1 + 3 e^{- t^{2}}} \]