I was messing around with a program I wrote to trace through slope fields using Euler's method, and I noticed this equation looked particularly funny: dy/dx=y−x/y*sin(y)

cofak48

cofak48

Answered question

2022-08-09

I was messing around with a program I wrote to trace through slope fields using Euler's method, and I noticed this equation looked particularly funny:
d y d x = y x y sin ( y )
Is there any solution, implicit or explicit?

Answer & Explanation

wijnvatid

wijnvatid

Beginner2022-08-10Added 16 answers

d y d x = y x y sin y
( y x ) d x d y = y sin y
Let u = y x,

Then x = y u
d x d y = 1 d u d y
u ( 1 d u d y ) = y sin y
u u d u d y = y sin y
u d u d y u = y sin y
This belongs to an Abel equation of the second kind in the canonical form.

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