23.2.155 problem 158

Internal problem ID [5510]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 158
Date solved : Tuesday, September 30, 2025 at 12:46:04 PM
CAS classification : [_separable]

\begin{align*} x^{2} {y^{\prime }}^{2}+3 x y^{\prime } y+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: 0.027 (sec). Leaf size: 26

ode=x^2 (D[y[x],x])^2+3 x y[x] D[y[x],x]+2 y[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: 0.092 (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)
 

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