What is the solution for y^{''}+ky=g-6t,y(0)=0,y^'(0)=0 ?

The solution for y^{''}+ky=g-6t,y(0)=0,y^'(0)=0 is y=-(6t)/k+(6sin(sqrt(k)t))/(ksqrt(k))

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y^{''}+ky=g-6t,y(0)=0,y^'(0)=0

y^{^{''}} + k y = g - 6 t, y (0) = 0, y^{^{'}} (0) = 0

y = - \frac{6 t}{k} + \frac{6 sin ( k t )}{k k}

Solution steps

y^{''} (t) + k y (t) = g - 6 t

Solve linear ODE:

y = - \frac{6 t}{k} + \frac{6 sin ( k t )}{k k}

y = - \frac{6 t}{k} + \frac{6 sin ( k t )}{k k}

y^{^{''}} + 8 y^{^{'}} + 16 y = 8 sin (4 x)

y^{^{''}} - 2 y^{^{'}} + y = (x^{2} - 2 x) e^{x}

y^{^{''}} + y^{^{'}} - 2 y = t e^{3 t}

y^{^{''}} + 24 y^{^{'}} + 144 y = t^{2} e^{- 12 t} + e^{- 12 t}

y^{^{''}} - 81 y = 3

What is the solution for y^{''}+ky=g-6t,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+ky=g-6t,y(0)=0,y^'(0)=0 is y=-(6t)/k+(6sin(sqrt(k)t))/(ksqrt(k))