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OpenStudy (anonymous):

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

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jimthompson5910 (jim_thompson5910):

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)

OpenStudy (anonymous):

awesome!! thanks so much :)

jimthompson5910 (jim_thompson5910):

yw

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