In: Advanced Math
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))