29.33.14 problem 976

Internal problem ID [5553]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 33
Problem number : 976
Date solved : Sunday, March 30, 2025 at 08:37:19 AM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.033 (sec). Leaf size: 31

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

\begin{align*} y &= \sqrt {-x^{2}+2 c_1} \\ y &= -\sqrt {-x^{2}+2 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 39

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

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

✓ Sympy. Time used: 0.413 (sec). Leaf size: 22

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

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