I don't know how to solve this initial value problem for math class... dy/dx = ycosx ; y(0)=1 please help!

Answer 1

NOTE EDITED ANSWER!

dy/dx = y*cosx

dy = y*cosx*dx

dy/y = cosx*dx

Integrate both sides:

ln(y) = sinx + C

make both sides a power of e

e^ln(y) = e^(sinx+C)

y(x) = e^C * e^sinx

Let K be a new constant = e^C

y(x) = K*e^sinx

****** EDIT *******

y(0) = k*e^0 = K = 1

Therefore K = 1

Answer 2

(1/y)dy = cosxdx

Integrate both sides

ln(y) = sinx + C

y = e^(sinx + C)

or, equivalently,

y = Ce^(sinx)

Answer 3

separate the y's and x's, then integrate & plug in initial value