Internal problem ID [13054]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {t^{2}}{y+y t^{3}}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(t),t)= t^2/(y(t)+t^3*y(t)),y(0) = -2],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\sqrt {36+6 \ln \left (t^{3}+1\right )}}{3} \]
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 26
DSolve[{y'[t]== t^2/(y[t]+t^3*y[t]),{y[0]==-2}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\sqrt {\frac {2}{3}} \sqrt {\log \left (t^3+1\right )+6} \]