In each of the following cases (a) - (c) the functions f (x) and g (x) are linea

Question

In each of the following cases (a) - (c) the functions f (x) and g (x) are linearly independent solutions of a second order constant coefficient homogeneous linear ode. For each case find the equation which the solutions satisfy and the general solution of the equation: (a) The two solutions satisfy f (x) g (x) = 1, f' (x) - 3f (x) = 0. (b) The solutions satisfy f (x)' = 3f (z) and g (x) = xf (x). (c) The solutions satisfy f' (x) = 3g and g' = -3f. (d) Write down the general solution of the equation: y" - 6y' + 10y = 0.

Explanation / Answer

d)

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