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1.49 Two particular solutions of the equation 4f''(z)+f(z)=4f'(z) are f1(z)=ez/2 and f2(z)=zez/2. a) Show that any...

1.49 Two particular solutions of the equation 4f''(z)+f(z)=4f'(z) are f1(z)=ez/2 and f2(z)=zez/2.

a) Show that any linear combination Af1(z) + Bf2(z) is also a valid solution to the differential equation.

b) Find the particular solution that satisfies the conditions f(2)=14e and f'(2)=12e.

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