74.4.38 problem 38

Internal problem ID [15931]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number : 38
Date solved : Tuesday, January 28, 2025 at 08:23:15 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y^{3}-y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.440 (sec). Leaf size: 16

dsolve(diff(y(t),t)=y(t)^3-y(t)^2,y(t), singsol=all)
 

\[ y = \frac {1}{\operatorname {LambertW}\left (-c_{1} {\mathrm e}^{t -1}\right )+1} \]

✓ Solution by Mathematica

Time used: 0.209 (sec). Leaf size: 40

DSolve[D[y[t],t]==y[t]^3-y[t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]^2}dK[1]\&\right ][t+c_1] \\ y(t)\to 0 \\ y(t)\to 1 \\ \end{align*}