88.5.8 problem 8

Internal problem ID [23982]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 35
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:48:56 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 0.047 (sec). Leaf size: 97

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

\begin{align*} y &= -\frac {\sqrt {-2 \sqrt {c_1^{2}+4 x^{2}}+2 c_1}}{2} \\ y &= \frac {\sqrt {-2 \sqrt {c_1^{2}+4 x^{2}}+2 c_1}}{2} \\ y &= -\frac {\sqrt {2 \sqrt {c_1^{2}+4 x^{2}}+2 c_1}}{2} \\ y &= \frac {\sqrt {2 \sqrt {c_1^{2}+4 x^{2}}+2 c_1}}{2} \\ \end{align*}

✓ Mathematica. Time used: 1.97 (sec). Leaf size: 106

ode=( x*y[x]  ) -( y[x]^4+x^2  )*D[y[x],{x,1}]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 2.320 (sec). Leaf size: 71

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

\[ \left [ y{\left (x \right )} = - \sqrt {C_{1} - \sqrt {C_{1}^{2} + x^{2}}}, \ y{\left (x \right )} = \sqrt {C_{1} - \sqrt {C_{1}^{2} + x^{2}}}, \ y{\left (x \right )} = - \sqrt {C_{1} + \sqrt {C_{1}^{2} + x^{2}}}, \ y{\left (x \right )} = \sqrt {C_{1} + \sqrt {C_{1}^{2} + x^{2}}}\right ] \]