60.1.427 problem 438

Internal problem ID [10441]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 438
Date solved : Sunday, March 30, 2025 at 04:43:36 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+3 x y y^{\prime }+2 y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 17

ode:=x^2*diff(y(x),x)^2+3*x*y(x)*diff(y(x),x)+2*y(x)^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 26

ode=2*y[x]^2 + 3*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^2} \\ y(x)\to \frac {c_1}{x} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.173 (sec). Leaf size: 12

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

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