74.8.28 problem 28

Internal problem ID [16164]
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 : 28
Date solved : Tuesday, January 28, 2025 at 08:53:19 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.182 (sec). Leaf size: 35

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

\begin{align*} y &= -\frac {\sqrt {6}\, t^{{3}/{2}}}{9} \\ y &= \frac {\sqrt {6}\, t^{{3}/{2}}}{9} \\ y &= c_{1} \left (-2 c_{1}^{2}+t \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 56

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

\begin{align*} y(t)\to c_1 \left (t-2 c_1{}^2\right ) \\ y(t)\to -\frac {1}{3} \sqrt {\frac {2}{3}} t^{3/2} \\ y(t)\to \frac {1}{3} \sqrt {\frac {2}{3}} t^{3/2} \\ \end{align*}