Internal problem ID [12574]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x^{\prime }-\frac {t^{2}}{x+t^{3} x}=0} \] With initial conditions \begin {align*} [x \left (0\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([diff(x(t),t)=t^2/(x(t)+t^3*x(t)),x(0) = -2],x(t), singsol=all)
\[ x \left (t \right ) = -\frac {\sqrt {6 \ln \left (t^{3}+1\right )+36}}{3} \]
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 26
DSolve[{x'[t]==t^2/(x[t]+t^3*x[t]),{x[0]==-2}},x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+6} \]