Question

prove the following

Answer 1

\[\text{ if } \frac{dy}{dx} = h(y)g(x)\] and
\[\text{ at } x = x_0 \text{ , } y =y_0\]

\[\int\limits_{y_0}^{y}{\frac{1}{h(y)}}dy = \int\limits_{x_0}^{x}{{g(x)}}dx\]

is equivalent to

\[\int\limits{\frac{1}{h(y)}}dy = \int\limits{g(x)}dx\]
where we substitute in x_0 and y_0 to find the arbitrary constants

Answer 2

is it clear what i am interested in knowing?

Answer 3

\(x\) is variable and \(x_0\) is constant?

Answer 4

Try differentiating.

Answer 5

There should be a restriction on h like h(x) is never zero.

Answer 6

yeah h(y) =/= 0

um i think i've sorted it out now