Find the solution to dy/dt = 7 y

satisfying
y(9) = 5

I'm not sure what methods you've learned up to this point but one option is to apply separation of variables:



and then integrate from there,



exponentiate to isolate y,



Apply exponent rule,



rename this e^c as some new constant, perhaps A,



This A can only be positive, non-zero, but absorbing the plus/minus fixes that restriction,



Use your initial information to solve for this unknown value A,



solving for A, dividing by the exponential,



So we get a final result of



apply exponent rule again to get a better looking answer, and factor,



Lemme know if too confusing.

I'm not sure sorry that i couldn't