What is the solution for f^{''}(t)-4f^'(t)+3f(t)=0,f(0)=3,f^'(0)=5 ?

The solution for f^{''}(t)-4f^'(t)+3f(t)=0,f(0)=3,f^'(0)=5 is f(t)=e^{3t}+2e^t

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f^{''}(t)-4f^'(t)+3f(t)=0,f(0)=3,f^'(0)=5

f^{^{''}} (t) - 4 f^{^{'}} (t) + 3 f (t) = 0, f (0) = 3, f^{^{'}} (0) = 5

f (t) = e^{3 t} + 2 e^{t}

Solution steps

f^{''} (t) - 4 f^{'} (t) + 3 f (t) = 0

Solve linear ODE:

f (t) = e^{3 t} + 2 e^{t}

f (t) = e^{3 t} + 2 e^{t}

What is the solution for f^{''}(t)-4f^'(t)+3f(t)=0,f(0)=3,f^'(0)=5 ?
The solution for f^{''}(t)-4f^'(t)+3f(t)=0,f(0)=3,f^'(0)=5 is f(t)=e^{3t}+2e^t