60.1.559 problem 573

Internal problem ID [10573]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 573
Date solved : Sunday, March 30, 2025 at 06:08:04 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 24

ode:=f(x*diff(y(x),x)^2)+2*x*diff(y(x),x)-y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_{1} +2 \operatorname {RootOf}\left (-f \left (\textit {\_Z}^{2}\right )-2 \textit {\_Z} +c_{1} +c_{2} \right ) \sqrt {x} \]

✓ Mathematica. Time used: 0.642 (sec). Leaf size: 48

ode=f[x*D[y[x],x]^2] - y[x] + 2*x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to f(c_1)-2 \sqrt {c_1} \sqrt {x} \\ y(x)\to f(c_1)+2 \sqrt {c_1} \sqrt {x} \\ y(x)\to f(0) \\ \end{align*}

✗ Sympy

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

NotImplementedError : multiple generators [_X0, f(_X0**2*x)] 
No algorithms are implemented to solve equation 2*_X0*x + f(_X0**2*x) - y(x)