47.2.25 problem 25

Internal problem ID [7441]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.2 Homogeneous equations problems. page 12
Problem number : 25
Date solved : Sunday, March 30, 2025 at 12:06:43 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: 15

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

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 24

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 c_1 x \\ y(x)\to c_1 x^2 \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.242 (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)
 

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