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Input:

y\'\'(x) + y(x) = 0


ODE classification:

second-order linear ordinary differential equation


Alternate form:

y\'\'(x) = -y(x)


Differential equation solution:

y(x) = c_2 sin(x) + c_1 cos(x)


Possible Lagrangian:

(script capital l)(y\', y) = 1\/2 (y\'^2 - y^2)

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