74.4.37 problem 37

Internal problem ID [15930]
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 : 37
Date solved : Tuesday, January 28, 2025 at 08:23:11 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 29

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

\begin{align*} y &= \frac {1}{\sqrt {c_{1} {\mathrm e}^{-2 t}-1}} \\ y &= -\frac {1}{\sqrt {c_{1} {\mathrm e}^{-2 t}-1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.199 (sec). Leaf size: 51

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

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