Taking a derivative of a differential equation and solving it is one approach to solving a differential equation. However, for some reason I can't get this method to work in cases where there is an interaction term.
Let's consider the differential equation:
Derived with respect to x we have:
$$y''+y'x+x'y = 0$$
$$\rightarrow y'' +y'x+y=0$$
If the differential equation is solved the answer is different for the equations above. Is there something that I am missing when taking the derivative of the equation?