I have attached the question below, and I solved it. Could you please control it ? Did I solve correct or not? If I did not solve correctly, could you please fix it and provide the correct solution of it? Thanks for your time.

EX let K (+ ) denote capital at time t. Suppose at time O, there is 1 unit capital This is on integral and K (0 ) = 1 its app peation Now consider the following two paths of capital ( a ) KC + ) - 0.02 K( + ) = 0 ( b ) K ( ) - 0.5 KC + ) = 0 Find solutions for both ( @) and (b). Solution K ' ( ) + 9 K ( ) = 0 d+ dk = _ ak => de =-adt integrating : JK = -a Sd+ log (14) = - 4+ + c At t= 0 , K = 1 = C=O - loge ( ) = - a - k = e - at