is dy/dx=5/x+y separable? If so, how?

Question

Thank You.

Answer 1

Is the given equation
dy/dx= (5/x) + y (≡ dy/dx=5/x+y)
or
dy/dx=5/(x+y) ?

Answer 2

it is dy/dx= (5/x) + y

Answer 3

An equation has separable variables if it can be rearranged to be in the following form:
A(x)dx + B(y)dy = 0 ....(1)
For example,
dy/dx = -y/x can be rewritten as
dy/y = -dx/x
Integrate both sides,
ln(y)=-ln(x)+C1
or
y=C/x where C is a constant.

The given equation cannot be rearranged to the form of equation (1), so it is not separable.

However, it can be solved with the integrating factor e^-x, resulting in
y=e^x*∫5e^-xdx/x

Answer 4

thanks =]