Internal problem ID [12617]
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 1.4 page 61
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-y^{2}+y^{3}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{5}}\right ] \end {align*}
✓ Solution by Maple
Time used: 1.391 (sec). Leaf size: 21
dsolve([diff(y(t),t)=y(t)^2-y(t)^3,y(0) = 1/5],y(t), singsol=all)
\[ y \left (t \right ) = \frac {1}{\operatorname {LambertW}\left (4 \,{\mathrm e}^{-t +4}\right )+1} \]
✓ Solution by Mathematica
Time used: 0.495 (sec). Leaf size: 31
DSolve[{y'[t]==y[t]^2-y[t]^3,{y[0]==2/10}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \text {InverseFunction}\left [\frac {1}{\text {$\#$1}}+\log (1-\text {$\#$1})-\log (\text {$\#$1})\&\right ][-t+5+\log (4)] \]