Question

Find a function y(t) so that the function satisfies
dydt=0.5y, y(2)=100

y(t)=?? HELP PLEASE

Answer 1

dy/dt = 0.5y


dy/y = 0.5*dt


int(dy/y) = int(0.5*dt)


ln|y| = 0.5t + C


|y| = e^(0.5t+C)


y = +-e^(0.5t+C)


y = +-e^C*(0.5t)


y = A*e^(0.5t)


------------------------

y(2) = 100, so...


100 = A*e^(2*0.5)


100/(e) = A


36.7879 = A


A = 36.7879


which means y(t) = 36.7879e^(0.5t)

Answer 2

awesome!! thanks so much :)

Answer 3

yw