29.26.24 problem 760

Internal problem ID [5345]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 760
Date solved : Tuesday, March 04, 2025 at 09:29:53 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.008 (sec). Leaf size: 23

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

\begin{align*} y \left (x \right ) &= {\mathrm e}^{\frac {x^{2}}{2}} c_{1} \\ y \left (x \right ) &= {\mathrm e}^{-\frac {x^{2}}{2}} c_{1} \\ \end{align*}

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 38

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

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

✓ Sympy. Time used: 0.417 (sec). Leaf size: 20

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

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