72.8.26 problem 39

Internal problem ID [14719]
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. Review Exercises for chapter 1. page 136
Problem number : 39
Date solved : Monday, March 31, 2025 at 12:55:17 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {t^{2}}{y+t^{3} y} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.082 (sec). Leaf size: 18

ode:=diff(y(t),t) = t^2/(y(t)+t^3*y(t)); 
ic:=y(0) = -2; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = -\frac {\sqrt {36+6 \ln \left (t^{3}+1\right )}}{3} \]

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 26

ode=D[y[t],t]== t^2/(y[t]+t^3*y[t]); 
ic={y[0]==-2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+6} \]

✓ Sympy. Time used: 0.499 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**2/(t**3*y(t) + y(t)) + Derivative(y(t), t),0) 
ics = {y(0): -2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = - \frac {\sqrt {6 \log {\left (t^{3} + 1 \right )} + 36}}{3} \]