15.21.6 problem 28

Internal problem ID [3330]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 28
Date solved : Monday, January 27, 2025 at 07:34:19 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 25

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

\begin{align*} y \left (x \right ) &= -\frac {4}{27 x^{2}} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= c_{1} x -c_{1}^{{2}/{3}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 23

DSolve[y[x]==D[y[x],x]*x-D[y[x],x]^(2/3),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 x-c_1{}^{2/3} \\ y(x)\to 0 \\ \end{align*}