Differential Equations Answers

Find the dy/dx, ify=sinx/cosx

sec^2x
sec2x
cosecx
coshx

Ify=e^5x. Determine dy/dx.

5e5x
4e^5x
e^5x
5e^5x

Find the dy/dx,ify=(sinx)^−1

tanx
cosx
cos^2
sinx

If y =
x^5.e^x, differentiate with respect to x

x^x e^x
x^4e^x(x−5)
x^4x
x^4e^x(x+5)

If y =
x4+5x3−4x2+7x−2 , differentiate with respect to x .

4x3+15x2−8x−7
4x3+15x2−8x+7
4x3+15x2−8x
2x-5

This problem should be solved using a differential equation:
A person is trying to fill a bathtub with water. Water is flowing into the bathtub from the tap at a constant rate of k litres/sec. However, there is a hole in the bottom of the bathtub and water is flowing out of the bathtub at a rate proportional to the square of the volume of water present in the bathtub. If V(t) is the volume of water (in litres) present in the bathtub at time t (in seconds) and the bathtub initially contains V(0) litres of water.

How can a differential equation of this problem b e written? (not solve just writing the equation)

Find all the roots of the equation X^3 +6X^2 +11X+6=0 by the Graeffe’s root squaring method using three squaring

The surface of a ball of radius A is kept at a temperature zero. If the initial temperature in the
ball is f (r), write down the boundary conditions and show that the temperature in the ball at
time t, u (r, t), is the solution to the equation:

c^2 ((∂^2 u)/(∂r^2 )+2/r ∂u/∂r)=∂u/∂t

Under what conditions the solution of the first order ordinary differential equation exist?

Furthermore, without solving the following initial value problem determine the interval in which the solution is certain to exist.

dy/dx + (tan x) y = sin x:y ( π/4) =0

Under what conditions the solution of the first order ordinary differential equation exist?

Furthermore, without solving the following initial value problem determine the interval in which the solution is certain to exist.

dy/dx + (tan x) y = sin x:y ( π/4) =0