What is the solution for y*α+(d^2y)/(dx^2)=0 ?

The solution for y*α+(d^2y)/(dx^2)=0 is y=c_{1}cos(sqrt(α)x)+c_{2}sin(sqrt(α)x)

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y*α+(d^2y)/(dx^2)=0

y \cdot α + \frac{d ^{2} y}{d x ^{2}} = 0

y = c_{1} cos (α x) + c_{2} sin (α x)

Solution steps

y \cdot α + \frac{d ^{2} y}{d x ^{2}} = 0

Solve linear ODE:

y = c_{1} cos (α x) + c_{2} sin (α x)

y = c_{1} cos (α x) + c_{2} sin (α x)

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

y^{^{''}} - 5 y^{^{'}} - 2 a^{2} y = 0

x^{^{''}} + 2 \cdot b \cdot x^{^{'}} + x = 0, x (0) = 1, x^{^{'}} (0) = - 1

y^{^{''}} - 4 π^{2} y = 0, y (0) = 0, y^{^{'}} (1) = 0

\frac{d ^{2} x}{d t ^{2}} = a (x)

What is the solution for y*α+(d^2y)/(dx^2)=0 ?
The solution for y*α+(d^2y)/(dx^2)=0 is y=c_{1}cos(sqrt(α)x)+c_{2}sin(sqrt(α)x)