What is the solution for y^{''}+16y=4(u 7/4 pi) ?

The solution for y^{''}+16y=4(u 7/4 pi) is y=c_{1}cos(4t)+c_{2}sin(4t)+(7piu)/(16)

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y^{''}+16y=4(u 7/4 pi)

y^{^{''}} + 16 y = 4 (u \frac{7}{4} π)

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{7 π u}{16}

Solution steps

y^{''} (t) + 16 y = 4 (u \frac{7}{4} π)

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{7 π u}{16}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{7 π u}{16}

y^{^{'''}} - y^{^{''}} - 4 y^{^{'}} + 4 y = - 20 t^{2} + 52 t - 6

y^{^{'''}} - 2 y^{^{''}} + 5 y^{^{'}} = - 24 e^{3 x}

y^{^{''}} + 4 y = 4 sec^{3} (2 t)

y^{^{''}} - 2 y^{^{'}} - 24 y = 6 e^{6 x}

y^{^{''}} + 36 y = 4 sin (2 x), y (0) = 1, y^{^{'}} (0) = 0

What is the solution for y^{''}+16y=4(u 7/4 pi) ?
The solution for y^{''}+16y=4(u 7/4 pi) is y=c_{1}cos(4t)+c_{2}sin(4t)+(7piu)/(16)