Form a differential equation if y=ae^-4x+be^-6x

Assuming A and B are constants, the trick for forming a differential equation when the original equation contains e is to keep each term the same and multiply by the derivative of the exponent.

For example, if your original function is y = Aeˣ + Beˣ, then the derivative, y', would be: y' = (Aeˣ)*x' + (Beˣ)*x'.

Therefore, for your equation, y' = -4Ae⁻⁴ˣ + -6Be⁻⁶ˣ.

Hope this helps!