29.27.5 problem 771

Internal problem ID [5355]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 771
Date solved : Sunday, March 30, 2025 at 08:02:40 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} {y^{\prime }}^{2}&=f \left (x \right )^{2} \left (y-u \left (x \right )\right )^{2} \left (y-a \right ) \left (y-b \right ) \end{align*}

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

ode=(D[y[x],x])^2==f[x]^2*(y[x]-u[x])^2*(y[x]-a)*(y[x]-b); 
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") 
u = Function("u") 
ode = Eq((a - y(x))*(-b + y(x))*(-u(x) + y(x))**2*f(x)**2 + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out