What is the solution for y^{''}-16y=7t,y(0)=0,y^'(0)=0 ?

The solution for y^{''}-16y=7t,y(0)=0,y^'(0)=0 is y= 7/128 e^{4t}-7/128 e^{-4t}-(7t)/(16)

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y^{''}-16y=7t,y(0)=0,y^'(0)=0

y^{^{''}} - 16 y = 7 t, y (0) = 0, y^{^{'}} (0) = 0

y = \frac{7}{128} e^{4 t} - \frac{7}{128} e^{- 4 t} - \frac{7 t}{16}

Solution steps

y^{''} (t) - 16 y = 7 t

Solve linear ODE:

y = \frac{7}{128} e^{4 t} - \frac{7}{128} e^{- 4 t} - \frac{7 t}{16}

y = \frac{7}{128} e^{4 t} - \frac{7}{128} e^{- 4 t} - \frac{7 t}{16}

What is the solution for y^{''}-16y=7t,y(0)=0,y^'(0)=0 ?
The solution for y^{''}-16y=7t,y(0)=0,y^'(0)=0 is y= 7/128 e^{4t}-7/128 e^{-4t}-(7t)/(16)