What is the solution for y^{''}+16y=e^{5t} ?

The solution for y^{''}+16y=e^{5t} is y=c_{1}cos(4t)+c_{2}sin(4t)+1/41 e^{5t}

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

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

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{41} e^{5 t}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{41} e^{5 t}

y = c_{1} cos (4 t) + c_{2} sin (4 t) + \frac{1}{41} 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)

\frac{d ^{2} x}{d t ^{2}} + 100 x = 36 cos (8 t)

What is the solution for y^{''}+16y=e^{5t} ?
The solution for y^{''}+16y=e^{5t} is y=c_{1}cos(4t)+c_{2}sin(4t)+1/41 e^{5t}