Question: Consider the differential equation xu (x + 1)u + u = 0. Suppose we know the solution to the initial value problem u(1) =

Consider the differential equation xu′′ − (x + 1)u′ + u = 0. Suppose we know the solution to the initial value problem u(1) = 2, u′(1) = 1 is u(x) = x + 1, while the solution to the initial value problem u(1) = 1, u′(1) = 1 is u(x) = e^x−1.

(a) What is the solution to the initial value problem u(1) = 3, u′(1) = −2?

(b) What is the general solution to the differential equation?

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a To find the solution to the initial value problem u1 3 u1 2 we can use the method of variation of ... View full answer

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