What is the solution for f^'(t)-f(t)=-7t,f(2)=-4 ?

The solution for f^'(t)-f(t)=-7t,f(2)=-4 is f(t)=7(t+1)-25e^{t-2}

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f^'(t)-f(t)=-7t,f(2)=-4

f^{^{'}} (t) - f (t) = - 7 t, f (2) = - 4

f (t) = 7 (t + 1) - 25 e^{t - 2}

Solution steps

f^{'} (t) - f (t) = - 7 t

Solve linear ODE:

f (t) = 7 (t + 1) - 25 e^{t - 2}

f (t) = 7 (t + 1) - 25 e^{t - 2}

\int \frac{2 y}{x ^{2} + y ^{2}} d x

\int e^{s i n (π x)} cos (π x) d x

\int_{0}^{3} \frac{- 6}{x x} d x

(1 - 5 y + x) y^{^{'}} + y = 5 x - 1

(\frac{1}{x})^{^{'}}

What is the solution for f^'(t)-f(t)=-7t,f(2)=-4 ?
The solution for f^'(t)-f(t)=-7t,f(2)=-4 is f(t)=7(t+1)-25e^{t-2}