What is the solution for y^{''}-6y=u^2(t),y(0)=0 ?

The solution for y^{''}-6y=u^2(t),y(0)=0 is y=-c_{2}e^{sqrt(6)t}+c_{2}e^{-sqrt(6)t}-(u^2t)/6

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y^{''}-6y=u^2(t),y(0)=0

y^{^{''}} - 6 y = u^{2} (t), y (0) = 0

y = - c_{2} e^{6 t} + c_{2} e^{- 6 t} - \frac{u ^{2} t}{6}

Solution steps

y^{''} (t) - 6 y = u^{2} (t)

Solve linear ODE:

y = - c_{2} e^{6 t} + c_{2} e^{- 6 t} - \frac{u ^{2} t}{6}

y = - c_{2} e^{6 t} + c_{2} e^{- 6 t} - \frac{u ^{2} t}{6}

y^{^{''}} + 16 y = e^{5 t}

y^{^{''}} + 256 y = 16 cos (3 x)

D (x) = - 6 (2940) + 4200

y^{^{''''}} - 16 y = 2 e^{- 2 x} + 3 e^{3 x} + cos (2 x) - 1

\frac{d ^{2}}{d t ^{2}} (θ (t)) + 4 θ (t) = cos (c^{2}) (2 t)

What is the solution for y^{''}-6y=u^2(t),y(0)=0 ?
The solution for y^{''}-6y=u^2(t),y(0)=0 is y=-c_{2}e^{sqrt(6)t}+c_{2}e^{-sqrt(6)t}-(u^2t)/6