29.4.16 problem 105

Internal problem ID [4707]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 4
Problem number : 105
Date solved : Tuesday, March 04, 2025 at 07:08:33 PM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }+\left (f \left (x \right )-y\right ) g \left (x \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") 
f = Function("f") 
g = Function("g") 
ode = Eq(sqrt((-a + y(x))*(-b + y(x)))*(f(x) - y(x))*g(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out