60.1.488 problem 501

Internal problem ID [10502]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 501
Date solved : Sunday, March 30, 2025 at 05:20:57 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 1.994 (sec). Leaf size: 48

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

\begin{align*} y &= 0 \\ y &= -\frac {\sqrt {-a d}\, \left (b x +c \right )}{a b} \\ y &= \frac {\sqrt {-a d}\, \left (b x +c \right )}{a b} \\ \end{align*}

✓ Mathematica. Time used: 69.621 (sec). Leaf size: 980

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

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

Timed Out