60.1.376 problem 385

Internal problem ID [10390]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 385
Date solved : Sunday, March 30, 2025 at 04:34:28 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} {y^{\prime }}^{2}-2 x^{2} y^{\prime }+2 x y&=0 \end{align*}

✓ Maple. Time used: 0.070 (sec). Leaf size: 161

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

\begin{align*} y &= \frac {x^{4}-\operatorname {RootOf}\left (x^{16}-12 \textit {\_Z}^{2} x^{12}+16 \textit {\_Z}^{3} x^{10}+30 \textit {\_Z}^{4} x^{8}-96 \textit {\_Z}^{5} x^{6}+100 \textit {\_Z}^{6} x^{4}-48 \textit {\_Z}^{7} x^{2}+9 \textit {\_Z}^{8}-16 c_1 \,x^{4}\right )^{2}}{2 x} \\ y &= \frac {x^{4}-\operatorname {RootOf}\left (x^{16}-12 \textit {\_Z}^{2} x^{12}-16 \textit {\_Z}^{3} x^{10}+30 \textit {\_Z}^{4} x^{8}+96 \textit {\_Z}^{5} x^{6}+100 \textit {\_Z}^{6} x^{4}+48 \textit {\_Z}^{7} x^{2}+9 \textit {\_Z}^{8}-16 c_1 \,x^{4}\right )^{2}}{2 x} \\ \end{align*}

✓ Mathematica. Time used: 60.483 (sec). Leaf size: 4749

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

Too large to display

✗ Sympy

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

NotImplementedError : The given ODE -x**2 - sqrt(x*(x**3 - 2*y(x))) + Derivative(y(x), x) cannot be solved by the factorable group method