Internal
problem
ID
[10728]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
Additional
non-linear
first
order
Problem
number
:
717
Date
solved
:
Monday, January 27, 2025 at 09:35:36 PM
CAS
classification
:
[[_1st_order, `_with_symmetry_[F(x),G(x)]`]]
✓ Solution by Maple
Time used: 0.265 (sec). Leaf size: 33
dsolve(diff(y(x),x) = -1/2*(x^2+x+a*x+a-2*(x^2+2*a*x+a^2+4*y(x))^(1/2))/(x+1),y(x), singsol=all)
✓ Solution by Mathematica
Time used: 0.766 (sec). Leaf size: 44
DSolve[D[y[x],x] == (-1/2*a - x/2 - (a*x)/2 - x^2/2 + Sqrt[a^2 + 2*a*x + x^2 + 4*y[x]])/(1 + x),y[x],x,IncludeSingularSolutions -> True]