2. Find a homogeneous linear differential equation with constant coefficients whose general solution is given. (1) y = C? + c?e³x (2) y = c?e-10x + C?xe-10x (3) y = C? cos 8x + c? sin 8x (4) y = C? ex cos x + c?ex sin x (5) y = C? + C?x + c3e7x (6) y = C? cos x + C? sin x + c3 cos 3x + c4 sin 3x

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2. Find a homogeneous linear differential equation with constant coefficients whose general solution is given. (1)

y = c_{1} + c_{2} e^{3 x}

(2)

y = c_{1} e^{? 10 x} + c_{2} x e^{? 10 x}

(3)

y = c_{1} cos 8 x + c_{2} sin 8 x

(4)

y = c_{1} e^{x} cos x + c_{2} e^{x} sin x

(5)

y = c_{1} + c_{2} x + c_{3} e^{7 x}

(6)

y = c_{1} cos x + c_{2} sin x + c_{3} cos 3 x + c_{4} sin 3 x

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