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Input:

y\'\'(x) + y(x) = sin(2 x)


ODE classification:

second-order linear ordinary differential equation


Differential equation solution:

y(x) = c_2 sin(x) + c_1 cos(x) - 1\/3 sin(2 x)


Possible Lagrangian:

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

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