Question #3f0a4

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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)#