What is the solution for y^{''}-y=15t,y(0)=-15t ?

The solution for y^{''}-y=15t,y(0)=-15t is y=c_{1}e^t+c_{2}e^{-t}-15t

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y^{''}-y=15t,y(0)=-15t

y^{^{''}} - y = 15 t, y (0) = - 15 t

y = c_{1} e^{t} + c_{2} e^{- t} - 15 t

Solution steps

y^{''} (t) - y = 15 t

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} - 15 t

y = c_{1} e^{t} + c_{2} e^{- t} - 15 t

x^{^{''}} + 6 x^{^{'}} + 5 x = sin (t)

2 \frac{d ^{2} y}{d x ^{2}} + 4 y^{^{'}} + 2 y = \frac{1}{e ^{x} ( x + 1 )}

y^{^{''}} + 4 y^{^{'}} + 4 y = 15 x + 17

y^{^{''}} + 16 y^{^{'}} + 64 y = 100 e^{2 x}

2 y^{^{''}} - 5 y^{^{'}} + 71.86 y = 4

What is the solution for y^{''}-y=15t,y(0)=-15t ?
The solution for y^{''}-y=15t,y(0)=-15t is y=c_{1}e^t+c_{2}e^{-t}-15t