Solving Differential Math Equations?

Posted on 2015-01-19 06:17:00 in Math by KEI

The differential equation

exp(y)dy/dx = (4x+4)/(-1siny+9cosy)

has an implicit general solution of the form F(x,y)= K

In fact, because the differential equation is separable, we can define the solution curve implicitly by a function in the form F(x,y)= G(x)+H(y)=K

Find such a solution and then give the related functions requested.

How I did it:

integral(e^y(-siny+9cosy))dy= integral(4x+4)dx

RHS = 2x(x+2)+C

LHS = e^y(4cosy+5siny)

F(x,y)= e^y(4cosy+5siny)-2x(x+2) = K

However, my answer is not correct.

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