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Answer 1 · 2016-08-09T00:44:19

$y = 3e^sin(x)$

Solving the separable differential equation, first we break up the terms into $f(x)dx = g(y)dy$ , and then integrate:

$dy/dx = ycos(x)$

$=> 1/ydy = cos(x)dx$

$=>int1/ydy = intcos(x)dx$

$=> ln(y) = sin(x)+C$

At $x=0, y=3$ :

$ln(3) = sin(0)+C$

$=> C = ln(3)$

$=> ln(y) = sin(x)+ln(3)$

$:. y = e^(sin(x)+ln(3))$

$=e^ln(3)e^sin(x)$

$=3e^sin(x)$