What is the solution for y^{''}+6y=t,y(0)=-3,y^'(0)=0 ?

The solution for y^{''}+6y=t,y(0)=-3,y^'(0)=0 is y=-3cos(sqrt(6)t)-1/(6sqrt(6))sin(sqrt(6)t)+t/6

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y^{''}+6y=t,y(0)=-3,y^'(0)=0

y^{^{''}} + 6 y = t, y (0) = - 3, y^{^{'}} (0) = 0

y = - 3 cos (6 t) - \frac{1}{6 6} sin (6 t) + \frac{t}{6}

Solution steps

y^{''} (t) + 6 y = t

Solve linear ODE:

y = - 3 cos (6 t) - \frac{1}{6 6} sin (6 t) + \frac{t}{6}

y = - 3 cos (6 t) - \frac{1}{6 6} sin (6 t) + \frac{t}{6}

3 y^{^{''}} + 2 y^{^{'}} + 1 = 0

y^{^{''}} - y^{^{'}} - 6 y = e^{- 3 x} (7 - 8 x + 6 x^{2})

y^{^{''}} - 2 y^{^{'}} + y = e^{t}, y (0) = 0, y^{^{'}} (0) = 9

y^{^{''}} - y = x^{2} e x + 3

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

What is the solution for y^{''}+6y=t,y(0)=-3,y^'(0)=0 ?
The solution for y^{''}+6y=t,y(0)=-3,y^'(0)=0 is y=-3cos(sqrt(6)t)-1/(6sqrt(6))sin(sqrt(6)t)+t/6