y'=6x^2/(2y+cosy))

necessaryh 2021-03-11 Answered

y=6x22y+cosy

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Expert Answer

Nathalie Redfern
Answered 2021-03-12 Author has 99 answers
This is a separable equation, which can be written as (2y+cosy)dy=6x2dx
Integrate: (2y+cosy)dy=6x2dx
LHS: (2y+cosy)dy=y2+siny+C1, where C1 is some constant.
RHS: 6x2dx=2x3+C2 where C2 is some constant.
So, from (1) it follows that y2+siny=2x3+C where we defined C as C2-C1
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