Help Please! Given the linear differential equation y\' + p(t) y =g(t) (1) The c

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Help Please!

Given the linear differential equation y' + p(t) y =g(t) (1) The corresponding homogeneous equation is y'+p(t)y =0 (2) Show that if x(t) and z(t) are solutions of (2), then u(t) = alpha x(t) + beta z(t) is also a solution of (2) for any numbers alpha and beta. Show that if y(t) is a solution of (1) and z(t) is a solution of (2), then v(t) = y(t) + z(t) is also a solution of (1). Conversely, show that if you find a solution y(t) of (1), then ANY solution v(t) of (1) can be written as v(t) = y(t) + z(t) (3)

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