60.1.359 problem 366

Internal problem ID [10373]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 366
Date solved : Sunday, March 30, 2025 at 04:30:36 PM
CAS classification : [_exact]

\begin{align*} f \left (x^{2}+a y^{2}\right ) \left (a y y^{\prime }+x \right )-y-x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 45

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

\[ -\frac {a y^{2} x}{\sqrt {a^{2} y^{2}}}-\int _{}^{-\frac {a y^{2}}{2}-\frac {x^{2}}{2}}f \left (-2 \textit {\_a} \right )d \textit {\_a} +c_1 = 0 \]

✓ Mathematica. Time used: 0.235 (sec). Leaf size: 91

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

\[ \text {Solve}\left [\int _1^{y(x)}\left (x-a f\left (x^2+a K[2]^2\right ) K[2]-\int _1^x\left (1-2 a K[1] K[2] f''\left (K[1]^2+a K[2]^2\right )\right )dK[1]\right )dK[2]+\int _1^x\left (y(x)-f\left (K[1]^2+a y(x)^2\right ) K[1]\right )dK[1]=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out