What is the solution for f^{''}(t)-f(t)=-8t,f(3)=-8 ?

The solution for f^{''}(t)-f(t)=-8t,f(3)=-8 is f(t)=e^{t-6}(-c_{2}-32e^3)+c_{2}e^{-t}+8t

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f^{''}(t)-f(t)=-8t,f(3)=-8

f^{^{''}} (t) - f (t) = - 8 t, f (3) = - 8

f (t) = e^{t - 6} (- c_{2} - 32 e^{3}) + c_{2} e^{- t} + 8 t

Solution steps

f^{''} (t) - f (t) = - 8 t

Solve linear ODE:

f (t) = e^{t - 6} (- c_{2} - 32 e^{3}) + c_{2} e^{- t} + 8 t

f (t) = e^{t - 6} (- c_{2} - 32 e^{3}) + c_{2} e^{- t} + 8 t

What is the solution for f^{''}(t)-f(t)=-8t,f(3)=-8 ?
The solution for f^{''}(t)-f(t)=-8t,f(3)=-8 is f(t)=e^{t-6}(-c_{2}-32e^3)+c_{2}e^{-t}+8t