89.31.4 problem 4

Internal problem ID [24949]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 246
Problem number : 4
Date solved : Thursday, October 02, 2025 at 11:36:29 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 4 {y^{\prime }}^{2} x +4 y y^{\prime }-y^{4}&=0 \end{align*}

✓ Maple. Time used: 0.132 (sec). Leaf size: 86

ode:=4*x*diff(y(x),x)^2+4*y(x)*diff(y(x),x)-y(x)^4 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{\sqrt {-x}} \\ y &= -\frac {1}{\sqrt {-x}} \\ y &= 0 \\ y &= \frac {\sqrt {x \operatorname {sech}\left (-\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )^{2}}\, \coth \left (-\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )}{x} \\ y &= -\frac {\sqrt {x \operatorname {sech}\left (-\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )^{2}}\, \coth \left (-\frac {\ln \left (x \right )}{2}+\frac {c_1}{2}\right )}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.284 (sec). Leaf size: 80

ode=4*x*D[y[x],x]^2+4*y[x]*D[y[x],x]-y[x]^4==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {2 e^{\frac {c_1}{2}}}{-x+e^{c_1}}\\ y(x)&\to \frac {2 e^{\frac {c_1}{2}}}{-x+e^{c_1}}\\ y(x)&\to 0\\ y(x)&\to -\frac {i}{\sqrt {x}}\\ y(x)&\to \frac {i}{\sqrt {x}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x*Derivative(y(x), x)**2 - y(x)**4 + 4*y(x)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out