How to approach the ODE y &#x2032; </msup> + sin &#x2061;<!-- ⁡ --> (

Esmeralda Lane

Esmeralda Lane

Answered question

2022-07-06

How to approach the ODE y + sin ( x + y ) = sin ( x y )

Answer & Explanation

esperoanow

esperoanow

Beginner2022-07-07Added 11 answers

y + sin ( x + y ) = sin ( x y )
y = sin ( x y ) sin ( x + y ) = 2 cos x sin y
d y d x = 2 cos x sin y
d y sin y = 2 cos x d x
csc y d y = 2 cos x d x
Integrating both sides, we get
ln | csc y cot y | = 2 sin x + c
where c is a constant of integration.

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