Please answer all parts of the following question. Please show all work and all steps. 1a.)...

Please answer all parts of the following question. Please show all work and all steps.

1a.) Solve the initial value problem W((t^2) + 1, f(t)) = 1, f(0) = 1

1b.) Let x1 and x2 be two solutions of x''+ ((x')/(t)) + q(t)x = 0, t > 0, where q(t) is a continuous function. Given that W(6)=7, find W(7)

1c.) Show that any solution of x''+ 5x' + 6x = 0 tends to zero as t approaches positive infinity.

1d.) Solve x'' + 2x' = 0, x(0) = 0, the limit as t approaches positive infinity x(t) = a

1e.) Solve x'' - x = t(e^(2t))

Expert Solution

Colby Messinger answered 6 months ago

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