54.1.429 problem 440

Internal problem ID [11743]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 440
Date solved : Tuesday, September 30, 2025 at 10:15:12 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+4 x y y^{\prime }-5 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

ode:=x^2*diff(y(x),x)^2+4*x*y(x)*diff(y(x),x)-5*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= c_1 x \\ y &= \frac {c_1}{x^{5}} \\ \end{align*}

✓ Mathematica. Time used: 0.028 (sec). Leaf size: 24

ode=-5*y[x]^2 + 4*x*y[x]*D[y[x],x] + x^2*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^5}\\ y(x)&\to c_1 x\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x)**2 + 4*x*y(x)*Derivative(y(x), x) - 5*y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \left [ y{\left (x \right )} = C_{1} x, \ y{\left (x \right )} = \frac {C_{1}}{x^{5}}\right ] \]