66.1.30 problem 33

Internal problem ID [15917]
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 : 33
Date solved : Thursday, October 02, 2025 at 10:30:00 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Maple. Time used: 0.083 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.082 (sec). Leaf size: 26

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

\begin{align*} x(t)&\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+6} \end{align*}

✓ Sympy. Time used: 0.335 (sec). Leaf size: 19

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

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