Internal
problem
ID
[11782]
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
:
Tuesday, January 28, 2025 at 06:11:23 PM
CAS
classification
:
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _reducible, _mu_y_y1]]
✓ Solution by Maple
Time used: 0.243 (sec). Leaf size: 41
dsolve((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,y(x), singsol=all)
✓ Solution by Mathematica
Time used: 0.965 (sec). Leaf size: 26
DSolve[-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,y[x],x,IncludeSingularSolutions -> True]