60.1.73 problem 74

Internal problem ID [10087]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 74
Date solved : Sunday, March 30, 2025 at 03:13:46 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

ode:=diff(y(x),x)-f(x)*(y(x)-g(x))*((y(x)-a)*(y(x)-b))^(1/2) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x] - f[x]*(y[x]-g[x])*Sqrt[(y[x]-a)*(y[x]-b)]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

Timed Out