15.21.5 problem 27

Internal problem ID [3329]
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 : 27
Date solved : Sunday, March 30, 2025 at 01:37:07 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} y&=y^{\prime } x +\frac {3}{{y^{\prime }}^{2}} \end{align*}

✓ Maple. Time used: 0.038 (sec). Leaf size: 70

ode:=y(x) = x*diff(y(x),x)+3/diff(y(x),x)^2; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {3 \,6^{{1}/{3}} \left (x^{2}\right )^{{1}/{3}}}{2} \\ y &= -\frac {3 \left (x^{2}\right )^{{1}/{3}} 2^{{1}/{3}} \left (i 3^{{5}/{6}}+3^{{1}/{3}}\right )}{4} \\ y &= -\frac {3 \left (x^{2}\right )^{{1}/{3}} 2^{{1}/{3}} \left (-i 3^{{5}/{6}}+3^{{1}/{3}}\right )}{4} \\ y &= c_1 x +\frac {3}{c_1^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 84

ode=y[x]==D[y[x],x]*x+3/D[y[x],x]^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 x+\frac {3}{c_1{}^2} \\ y(x)\to -\frac {3 \sqrt [3]{-3} x^{2/3}}{2^{2/3}} \\ y(x)\to \frac {3 \sqrt [3]{3} x^{2/3}}{2^{2/3}} \\ y(x)\to \frac {3 (-1)^{2/3} \sqrt [3]{3} x^{2/3}}{2^{2/3}} \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + y(x) - 3/Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out