74.8.24 problem 24

Internal problem ID [16160]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 08:53:09 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 39

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

\begin{align*} y &= -\frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{-2 t}-4 t}} \\ y &= \frac {2}{\sqrt {2+4 c_{1} {\mathrm e}^{-2 t}-4 t}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.185 (sec). Leaf size: 73

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

\begin{align*} y(t)\to -\frac {e^t}{\sqrt {-2 \int _1^te^{2 K[1]} K[1]dK[1]+c_1}} \\ y(t)\to \frac {e^t}{\sqrt {-2 \int _1^te^{2 K[1]} K[1]dK[1]+c_1}} \\ y(t)\to 0 \\ \end{align*}