60.1.236 problem 241

Internal problem ID [10250]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 241
Date solved : Wednesday, March 05, 2025 at 08:49:05 AM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 29

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

\begin{align*} y &= \sqrt {\left (-a x +c_{1} \right ) x} \\ y &= -\sqrt {\left (-a x +c_{1} \right ) x} \\ \end{align*}

✓ Mathematica. Time used: 0.388 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 0.509 (sec). Leaf size: 26

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

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