Question

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

Give the largest interval over which the general solution is defined. (Think about the implications of any singular points. Enter your answer using interval notation.)

Determine whether there are any transient terms in the general solution.

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.