54.7.166 problem 1784 (book 6.193)

Internal problem ID [13015]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 6, non-linear second order
Problem number : 1784 (book 6.193)
Date solved : Friday, October 03, 2025 at 03:58:19 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} \left (x +y^{2}\right ) y^{\prime \prime }-2 \left (x -y^{2}\right ) {y^{\prime }}^{3}+y^{\prime } \left (1+4 y y^{\prime }\right )&=0 \end{align*}

✓ Maple. Time used: 0.124 (sec). Leaf size: 37

ode:=(x+y(x)^2)*diff(diff(y(x),x),x)-2*(x-y(x)^2)*diff(y(x),x)^3+diff(y(x),x)*(1+4*y(x)*diff(y(x),x)) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \sqrt {-x} \\ y &= -\sqrt {-x} \\ c_1 y+\ln \left (x +y^{2}\right )-c_2 +2 &= 0 \\ \end{align*}

✗ Mathematica

ode=-2*(x - y[x]^2)*D[y[x],x]^3 + D[y[x],x]*(1 + 4*y[x]*D[y[x],x]) + (x + y[x]^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + y(x)**2)*Derivative(y(x), (x, 2)) - (2*x - 2*y(x)**2)*Derivative(y(x), x)**3 + (4*y(x)*Derivative(y(x), x) + 1)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out