Question

Determine all solutions of the differential equation y' = -9 y. Use the variables C and x as appropriate.

Answer 1

If y ' = -9y

then to find y, you want the integral of -9y which is

-9y^2/2 + C

Answer 2

Express the logarithm equation in exponential form.

ln(x + 1) = 2

Answer 3

I am on the struggle

Answer 4

nvm I figured it out

Answer 5

Your welcome.

Answer 6

\[\Large \frac{dy}{dx}=-9y\qquad\to\qquad \frac{dy}{y}=-9dx\]Integrating:\[\Large \ln y=-9x+c\]Exponentiating:\[\Large y=e^{-9x+c}\qquad\to\qquad y=e^{-9x}\cdot e^c\]Simplifying:\[\Large y=Ce^{-9x}\]