Differential Equations Answers

Can anyone help me with this question? I've been trying to find ways to solve it but I have not found the correct way on how to. I hope you can help me with this question.

"Two points are moving horizontally in space at different heights above the earth. Show that the angle of elevation of the line joining them is greater when the distance between them is least."

Integrate W.R.T x:
e^x(1+1/x)
Explain with steps please

differentiate W.R.T x :
e rest to xlogx means e^xlogx (xlogx in power of e)

please explain with steps

Find the critical points and test for the maximun and minimum. y=x^3+3x^2+6x-4

y[sup]2[/sup] e[sup]2x[/sup] + log(3,y) = 2xln y

Given y(0) = 2 and y'(0) = 3.
Solve for the Laplace transform Y(s) using the differential equation below.

y'' - 2y' + y = 0

Is x = 3 an asymptote of the function f(x)= (x[sup]2[/sup] -5x+6)/(x-3)? Why?

What would the future value of $6.5 million dollars be after 5 years at 1.2% interest rate?

Solve y''=(y')[sup]2[/sup] +y[sup]2[/sup]

solve my differential equation
y'' =(y')[sup]3[/sup] + x[sup]2[/sup]