Question: (a) Given that y = sin x is a solution of y (4) + 2y''' + 11y'' + 2y' + 10y = 0, find the

(a) Given that y = sin x is a solution of

y⁽⁴⁾ + 2y''' + 11y'' + 2y' + 10y = 0,

find the general solution of the DE without the aid of a calculator or a computer.

(b) Find a linear second-order differential equation with constant coefficients for which y₁ = 1 and y₂ = e^-x are solutions of the associated homogeneous equation and y_p = 1/2x² - x is a particular solution of the nonhomogeneous equation.

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