What is the solution for (D^2+64)^2y=0 ?

The solution for (D^2+64)^2y=0 is y=c_{1}cos(8x)+c_{2}sin(8x)+x(c_{3}cos(8x)+c_{4}sin(8x))

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(D^2+64)^2y=0

(D^{2} + 64)^{2} y = 0

y = c_{1} cos (8 x) + c_{2} sin (8 x) + x (c_{3} cos (8 x) + c_{4} sin (8 x))

Solution steps

(D^{2} + 64)^{2} y = 0

Solve linear ODE:

y = c_{1} cos (8 x) + c_{2} sin (8 x) + x (c_{3} cos (8 x) + c_{4} sin (8 x))

y = c_{1} cos (8 x) + c_{2} sin (8 x) + x (c_{3} cos (8 x) + c_{4} sin (8 x))

y^{^{''}} = a^{2} y

4 \cdot \frac{d ^{2} y}{d x ^{2}} + 12 \cdot \frac{d y}{d x} + 9 y = 0

y^{^{''}} - 5 y^{^{'}} + 6 y = 0, y (0) = \frac{2}{3}

0.2 q^{^{''}} + 4 q^{^{'}} + 100 q = 0

y^{^{''}} - 20 y^{^{'}} + 100 y = 0, y (0) = 4, y (1) = 3

What is the solution for (D^2+64)^2y=0 ?
The solution for (D^2+64)^2y=0 is y=c_{1}cos(8x)+c_{2}sin(8x)+x(c_{3}cos(8x)+c_{4}sin(8x))