Differential EQNS: $y \, dx = \left[ x + (y^2 - x^2)^{1/2} \right] dy$
ydx = x + √ y^2 - x^2 dy
July 2016
Differential Calculus: largest cone inscribed in a sphere
Find the dimensions of the largest circular cone that can be inscribed in a sphere of radius R.
Differential Calculus: Cylinder of largest lateral area inscribed in a sphere
Find the ratio of the altitude h to the base radius r of a right circular cylinder having the largest lateral surface area S, if the right circular cylinder is to be inscribed in a sphere of radius R.
differential equations: $y(9x - 2y)dx - x(6x - y)dy = 0$
y(9x -2y)dx - x(6x - y) dy = 0
Differential Equations: $[x \csc (y/x) - y] dx + x \, dy = 0$
2. (x csc y/x - y) dx + xdy=0
3. (x^2 + 2xy - 4y^2) dx - ( x^2 - 8xy - 4 y^2)=0
4. x^y ' = 4x^2 + 7xy + 2 y^2
Differential Equations: $(6x-3y+2)dx - (2x-y-1)dy = 0$
Help a stranger please. This is for my homework and I'm having a hard time solving these equations. Show the complete solutions and final answers please. It will be a great help. Thank you so much.
This covers Additional Topics on Equations of Order One, Coefficient Linear in Two Variables.
1. (6x-3y+2)dx-(2x-y-1)dy=0
2. (x+2y-1)dx-(2x+y-5)dy=0
Area the goat can graze inside a right triangular lot
Problem
A 30° right triangular lot has the long leg measuring 67 m. On the long leg and 15 m from the short leg, is a peg to which a goat is tied such that the farthest distance its mouth can reach is 30 m from the peg. Find the area inside the lot from which the goat can graze.
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Example 8 | Area bounded by arcs of quarter circles
Problem
Arcs of quarter circles are drawn inside the square. The center of each circle is at each corner of the square. If the radius of each arc is equal to 20 cm and the sides of the square are also 20 cm. Find the area common to the four circular quadrants. See figure below.
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diffirential equations: how to eliminate arbitrary constant where h is a parameter; y=mx+h/m
please help
how to eliminate arbitrary constant where h is a parameter;
y=mx+h/m
Elimination of arbitrary constants: $y = Ae^{ax} \cos (bx) + Be^{ax} \sin (bx)$
Im having a difficulty solving this problem y = Aeaxcos(bx)+Beaxsin(bx) where a and b are parameters. Can anyone show me how to solve this ?