Differential Calculus

1. (D^5 + D^4 − 7D^3 − 11D^2 − 8D − 12)y = 0.
2. (D^4 − 2D^3 + 2D^2 − 2D + 1)y = 0.

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

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.

solve for homogeneous

ydx = [ x + (y^2 - x^2)^1/2] dy

pa help naman poh pls

A mold grows at a rate proportional to its present size. Initially there is 2 oz of this mold,
and two days later there is 3 oz. Find (a) how much mold was present after one day and (b)
how much mold will be present in ten days.
pls answer this probem..

Paano po malalaman kung kailan i dederive yung sa Application ng maxima and minima, meron po kasing instances na sa una nag dederive na pero yung iba naman sinisimplify lang as in terms or y or x.

A boatman is at which is 4.51cm from the nearest point B on A straight shore. He wishes to reach in Minimum time a point C. Situated on the shore 9km from B. How far from C should He land if He can now at the rate of 6kph and walk at the rate of 7.5kph.

The base of triangle is on the X-axis, one side lies along the line y=3x, and the third side passes through the point (1,1).what is the slope of the third side if the area of the triangle is to be a minimum.

hy,
i've studied limit and continuity more than 10 times but my concept is still not very clear , can any one help?