Question

find dy/dx for ln(5y)=e^y sin(5x)

Answer 1

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Answer 2

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Answer 3

find dy/dx for ln(5y)=e^y sin(5x)
Dln(5y)=D[e^y sin(5x)]
5y'/5y =e^y(5cos5x)+(sin5x)y'e^y
y'/y-(sin5x)y'e^y=e^y(5cos5x) factoring out y' we get
y'(1/y-(sin5x)e^y)=5e^y(cos5x)
y'=5e^y(cos5x) /[(1/y)-(sin5x)e^y)] or

y'=5/[(1/ye^ycos5x-tan5x)]