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}

y^{^{''}} + y^{^{'}} + 2 y - x - 3 = 0, y (0) = 0

\frac{d ^{2} x}{d t ^{2}} - 3 \frac{d x}{d t} + 2 x = e^{t}

y^{^{''}} - y = sin (3 x)

5 y^{^{''}} - 19 y^{^{'}} - 4 y = 1 + 4 x

(d^{3} - 7 d - 6) y = 2 e^{x} cos (\frac{x}{2})

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)