72.1.29 problem 32

Internal problem ID [14550]
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. Exercises section 1.2. page 33
Problem number : 32
Date solved : Thursday, March 13, 2025 at 03:33:39 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.089 (sec). Leaf size: 16

ode:=diff(y(t),t) = t*y(t)^2+2*y(t)^2; 
ic:=y(0) = 1; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\frac {2}{t^{2}+4 t -2} \]

✓ Mathematica. Time used: 0.138 (sec). Leaf size: 17

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

\[ y(t)\to -\frac {2}{t^2+4 t-2} \]

✓ Sympy. Time used: 0.203 (sec). Leaf size: 14

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

\[ y{\left (t \right )} = - \frac {2}{t^{2} + 4 t - 2} \]