Question

Find the general solution of the given differential equation. dy/dx = 9yy(x) = ?

Answer 1

Answer:

See answer below

Step-by-step explanation:

This is a separable equation, so we solve it like this:

$\frac{dy}{y}=9dx \implies (\ln(y))'=9dx \implies ln(y)=9x+c \implies y=e^{9x+c} \implies y=ke^{9x}$

Then $y(x)=ke^{9x}$ for any constant k (this is the general solution). This solution is defined in (-∞,∞) (there are no singularities) and when x tends to infinity, no terms of the solution vanish, hence there are no transient terms.