74.7.48 problem 51

Internal problem ID [16125]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 51
Date solved : Tuesday, January 28, 2025 at 08:50:17 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.148 (sec). Leaf size: 35

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

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

✓ Solution by Mathematica

Time used: 0.007 (sec). Leaf size: 52

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

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