Internal problem ID [12917]
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 1.3 page 47
Problem number: 16 (iii).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{3}-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.172 (sec). Leaf size: 18
dsolve(diff(y(t),t)=y(t)^3+y(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = -\frac {1}{\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{t -1}\right )+1} \]
✓ Solution by Mathematica
Time used: 0.318 (sec). Leaf size: 38
DSolve[y'[t]==y[t]^3+y[t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \text {InverseFunction}\left [-\frac {1}{\text {$\#$1}}-\log (\text {$\#$1})+\log (\text {$\#$1}+1)\&\right ][t+c_1] \\ y(t)\to -1 \\ y(t)\to 0 \\ \end{align*}