Solve by determining the general form the function might take and then evaluating some coefficients. dy/dt+2y=exp(5t)

since it is a first orderedlinear ODE first we look for M(t)=e^integral(2)=e^2t then multiplying whole equation by M will give d[(e^(2t))*y]/dt=e^(5t) * e^(2t) d[(e^(2t))*y]=e^(7t) dt integrating both sides gives (e^(2t))*y=(e^(7t))/7 +C solving the result for y gives y= (e^(5t))/7 +C(e^(-2t)) that is the general solution of the diff. equ.

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: