February 2016

Thank you for this site. I can now understand the lessons :)

(sin x)y''' − 3xy'' + 2y = tan x

find yhe dimension of right circular cylinder of maximum lateral surface area which can be inscribed in a sphere of radius 4 in.

arc cos x = π/2 - arc sin x

Show that if f and f' are continuous on a ≤ x ≤ b and f(x) is not zero for all x on a ≤ x ≤ b,
then f and xf are linearly independent on a ≤ x ≤ b.

Let
f1(x) = 1 + x^3 for x ≤ 0 ,1 for x ≥ 0
f2(x)= 1 for x ≤ 0, 1 + x^3 for x ≥ 0
f3(x)= 3 + x^3 for all x.

show that
a) f, f' , f", are continous for all x for each f1, f2, f3.

The given two-parameter family is a solution of the indicated differential equation on the
interval (−∞,∞). Determine whether a member of the family can be found that satisfies the
initial conditions.
y = c1e^x cos x + c2e^x sin x; y" − 2y' + 2y = 0,
i. y(0) = 1, y'(π) = 0
ii. y(0) = 1, y(π) = −1