60.1.490 problem 503

Internal problem ID [10504]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 503
Date solved : Sunday, March 30, 2025 at 05:22:45 PM
CAS classification : [_rational]

\begin{align*} \left (\operatorname {b2} y+\operatorname {a2} x +\operatorname {c2} \right )^{2} {y^{\prime }}^{2}+\left (\operatorname {a1} x +\operatorname {b1} y+\operatorname {c1} \right ) y^{\prime }+\operatorname {b0} y+\operatorname {a0} +\operatorname {c0}&=0 \end{align*}

✗ Maple

ode:=(b2*y(x)+a2*x+c2)^2*diff(y(x),x)^2+(a1*x+b1*y(x)+c1)*diff(y(x),x)+b0*y(x)+a0+c0 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=a0 + c0 + b0*y[x] + (c1 + a1*x + b1*y[x])*D[y[x],x] + (c2 + a2*x + b2*y[x])^2*D[y[x],x]^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a0 = symbols("a0") 
a1 = symbols("a1") 
a2 = symbols("a2") 
b0 = symbols("b0") 
b1 = symbols("b1") 
b2 = symbols("b2") 
c0 = symbols("c0") 
c1 = symbols("c1") 
c2 = symbols("c2") 
y = Function("y") 
ode = Eq(a0 + b0*y(x) + c0 + (a1*x + b1*y(x) + c1)*Derivative(y(x), x) + (a2*x + b2*y(x) + c2)**2*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out