Internal
problem
ID
[10885]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
875
Date
solved
:
Tuesday, January 28, 2025 at 05:28:32 PM
CAS
classification
:
[[_1st_order, `_with_symmetry_[F(x),G(x)*y+H(x)]`]]
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 74
dsolve(diff(y(x),x) = -(-x*y(x)-y(x)+x^5*(y(x)^2+x^2)^(1/2)-x^4*(y(x)^2+x^2)^(1/2)*y(x))/x/(x+1),y(x), singsol=all)
✓ Solution by Mathematica
Time used: 37.175 (sec). Leaf size: 232
DSolve[D[y[x],x] == (y[x] + x*y[x] - x^5*Sqrt[x^2 + y[x]^2] + x^4*y[x]*Sqrt[x^2 + y[x]^2])/(x*(1 + x)),y[x],x,IncludeSingularSolutions -> True]