Question

What is a solution to the differential equation `dy/dx=y/x`?

Answer 1

`y=Cx`

Explanation:

We can separate the variables:

`dy/dx=y/x" "=>" "dy/y=dx/x`

Integrate both sides:

`intdy/y=intdx/x" "=>" "ln(y)=ln(x)+C`

So:

`y=e^(ln(x)+C)=e^ln(x)*e^C=Cx`