60.1.472 problem 485

Internal problem ID [10486]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 485
Date solved : Sunday, March 30, 2025 at 05:04:01 PM
CAS classification : [_rational]

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

✗ Maple

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

\[ \text {No solution found} \]

✓ Mathematica. Time used: 3.65 (sec). Leaf size: 155

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

\begin{align*} y(x)\to \sqrt {c_1 \left (x^2+\frac {c}{b-a c_1}\right )} \\ y(x)\to -\sqrt {-\frac {\left (\sqrt {c}+i \sqrt {b} x\right )^2}{a}} \\ y(x)\to \sqrt {-\frac {\left (\sqrt {c}+i \sqrt {b} x\right )^2}{a}} \\ y(x)\to -\sqrt {-\frac {\left (\sqrt {c}-i \sqrt {b} x\right )^2}{a}} \\ y(x)\to \sqrt {-\frac {\left (\sqrt {c}-i \sqrt {b} x\right )^2}{a}} \\ \end{align*}

✗ Sympy

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

Timed Out