72.1.30 problem 33

Internal problem ID [14630]
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 : Tuesday, January 28, 2025 at 06:45:14 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*}

✓ Solution by Maple

Time used: 0.096 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 26

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

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