51.1.52 problem 52

Internal problem ID [10322]
Book : First order enumerated odes
Section : section 1
Problem number : 52
Date solved : Tuesday, September 30, 2025 at 07:19:24 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 27

ode:=diff(y(x),x)^2 = y(x)^2/x; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= 0 \\ y &= c_1 \,{\mathrm e}^{-2 \sqrt {x}} \\ y &= c_1 \,{\mathrm e}^{2 \sqrt {x}} \\ \end{align*}

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 38

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

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

✓ Sympy. Time used: 0.266 (sec). Leaf size: 31

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

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