60.1.468 problem 481

Internal problem ID [10482]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 481
Date solved : Sunday, March 30, 2025 at 05:00:29 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 35

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

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

✓ Mathematica. Time used: 0.142 (sec). Leaf size: 54

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

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

✓ Sympy. Time used: 0.542 (sec). Leaf size: 27

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

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