What is the solution for (d^2y)/(dx^2)-4 derivative of 4+4y=0 ?

The solution for (d^2y)/(dx^2)-4 derivative of 4+4y=0 is y=c_{1}cos(2x)+c_{2}sin(2x)

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(d^2y)/(dx^2)-4 derivative of 4+4y=0

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d}{d x} (4) + 4 y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d}{d x} (4) + 4 y = 0

Solve linear ODE:

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

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

- 0.0375 x^{^{''}} + 0.4535 x^{^{'}} + 3.34 x = 0

y^{^{'}} = 7 y^{^{''}}

6 y^{^{'''}} + 78 y^{^{'}} - 696 y = 0

y^{^{''}} - \frac{1}{a ^{2}} y = 0

y^{^{''}} + y^{^{'}} - 6 y = 0, y (0) = - 3

What is the solution for (d^2y)/(dx^2)-4 derivative of 4+4y=0 ?
The solution for (d^2y)/(dx^2)-4 derivative of 4+4y=0 is y=c_{1}cos(2x)+c_{2}sin(2x)