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Homework Statement 1. Using series solution to solve dy/dx - y(x) = x where y(0) = -1. [y(x) = Σ ak x^k from 0 to infinity. 2 Find c0 and c1 in y(x) = c0 e^αx + c1 e^-αx so that y(x) = a0 cosh(αx) +(a1/α) sinh (αx) 3. Find the 2 independent solutions of x d2y/dx2 + 2 dy/dx +xy = 0 using the...

Homework Statement 1. Prove that the sequence sqrt(n+1) - sqrt(n) converges to 0. 2. If sequence {an} is composed of real numbers and if lim as n goes to infinity of {a2n} = A and the limit as n goes to infinity of {a(2n-1)} = A, prove that {an} converges to 1. Is converse true? 3. Consider...