What is the solution for y^{''}-16y=6,y(0)=1 ?

The solution for y^{''}-16y=6,y(0)=1 is y=(-c_{2}+11/8)e^{4t}+c_{2}e^{-4t}-3/8

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y^{''}-16y=6,y(0)=1

y^{^{''}} - 16 y = 6, y (0) = 1

y = (- c_{2} + \frac{11}{8}) e^{4 t} + c_{2} e^{- 4 t} - \frac{3}{8}

Solution steps

y^{''} (t) - 16 y = 6

Solve linear ODE:

y = (- c_{2} + \frac{11}{8}) e^{4 t} + c_{2} e^{- 4 t} - \frac{3}{8}

y = (- c_{2} + \frac{11}{8}) e^{4 t} + c_{2} e^{- 4 t} - \frac{3}{8}

y^{^{'''}} - 6 y^{^{''}} + 32 y = e^{4 x}

y^{^{''}} + 5 y^{^{'}} + 4 y = 6 e^{- x} + cos (2 x)

y^{^{''}} + 4 y = t^{2} + 8 e^{t}, y (0) = 0, y^{^{'}} (0) = 1

y^{^{'''}} + 49 y^{^{'}} = tan (7 x)

y^{^{''}} + a y^{^{'}} = e^{3 t}

What is the solution for y^{''}-16y=6,y(0)=1 ?
The solution for y^{''}-16y=6,y(0)=1 is y=(-c_{2}+11/8)e^{4t}+c_{2}e^{-4t}-3/8