Using the reduction of order method second linearly independent
Given that y=e^x is a solution to: (x-1)*y'' -x*y' + y=0 x>1 Using the reduction of order method find a second linearly independent solution
Given that y=e^x is a solution to: (x-1)*y'' -x*y' + y=0 x>1 Using the reduction of order method find a second linearly independent solution
A farmer has 480 meters of fencing. He wishes to enclose a rectangular plot of land and to divide the plot into three equal rectangles with two parallel lengths of fence down the middle. What dimensions will maximize the enclosed area? Be sure to verify that you have found the maximum enclosed area.
See attached file for full problem description. Find a function f(x) = x^k and a function g such that f(g(x)) = h(x) = sqrt(3x+ x^2)
A car is moving from left to right along a road which lies along the straight line 3x + 4y = 12 in the xy-plane. (The x and y coordinates are measured in miles.) The following short table gives the x-coordinate of the car at several times: t 3:00pm 3:10pm 3:15pm 3:30pm 4:00pm x -28 -24
(Parabaloid of revolution) Determine the shape assumed by the surface of a liquid being spun in a circular bowl at constant angular velocity, W. Hint: consider a particle of liquid located at (x, y) on the surface of the liquid. The forces acting on the particle are m*W^2*x in the x direction and -m*g in the y direction.
1. A tank with a capacity of 500 gal. originally contains 200 gal. of water with 100 lb. of salt in solution. Water containing 1 lb. of salt per gallon is entering at the rate of 3 gal./min. and the mixture flows out at a rate of 2 gal./min. (i) Write a differential equation for the concentration in the tank before the tank o
Finding tangent line for f(x) that pass through the given point ( and the point isn't on the curve) part 1 f(X) = 4x-x^2; (2,5) Part 2 f(x) =x^2; (1,-3)
A 24 foot chain, weighing Y lbs/foot of length, is stretched out on a very tall frictionless table with 6 feet hanging over the edge of the table. If the chain is released from rest , in the configuration described above, find the following: a) How long before the chain falls off the table? b) What is the velocity of the cha
Find the present value and future value of an income stream of $1000 a year, for a period of 5 years, if the interest rate is 8%
There is a vat of wine with a tap at the bottom and a water faucet at the top. The tap is open and draining wine at a certain rate. The water faucet is adding water at the same rate, keeping the volume the same. How do I determine the concentration of the wine for any moment?
There is a vat of wine with a tap at the bottom and a water faucet at the top. The tap is open and draining wine at a certain rate. The water faucet is adding water at the same rate, keeping the volume the same. How do I determine the concentration of the wine for any moment?
Find the radius of convergence of About x= (-1/3) Thanks! Please see the attached file for the fully formatted problem.
Consider a right cylinderical hot tub. Radius = 5 feet; Height = 4 feet; placed on one of its circular ends. water is draining from the tub through a circular hole in the base of the tub 5/8inches in diameter. k = .6; using Torricelli's Law v = [2*g*h(t)]^1/2 and the equation dV/dt = -kAv where A is the are
Verify that (1+x) and e^x are solutions to the homogeneous equation corresponding to xy'' -(1+x)y'+y=x^2 e^2x, x>0 and find the general solution. Book give an answer of Y(x)=1/2(x-1)e^2x
Y'=ty^3 with y(0)= -1 over [-3/4, 3/4] Having trouble solving for y
(See attached file for full problem description) --- If - ∫3b 3x2 dx = 37 Then find the value of b. Note - The b is supposed to be directly over the 3.
The Lennard-Jones potential for the interaction of two molecules separated by distance R is U(R)= A/R^12 - B/R^6 where A and B are constants. the equilibrium separation Re is that value of R at which u(R) is a minimum and the binding energy is De = -U(Re). Express: (a) A and B in terms of Re and De. (b) U(R) in terms of R,
Verify that e^x and x are solutions to the homogeneous equation corresponding to (1-x)y"+xy'-y=2(x-1)^2e^-x ; 0<x<1 And find the general solution
Determine the particular solution of the following nonhomogeneous differential equation using the method of variation of parameters y" + 4y' + 4y = x^-2 e^-2x ; x>0 homogeneous equation is y =C1e^-2x +C2xe^-2x y= u1e^-2x +u2xe^-2x after differentiating and letting u'1e^-2x +u'2xe^-2x =0, we have _2u'e^-2x -2'u2xe^-2
A $100,000 mortgage is to be paid over 15 years at 7.4% per annum, compounded semi-annually, with monthly payments. What are the monthly payments (to the nearest dollar)?
Consider two tanks, labeled Tank A and Tank B. Tank A contains 100 gallons of solution in which is dissolved 20 lbs of salt. Tank B contains 200 gallons of solution in which is dissolved 40 lbs of salt. Pure water flows into tank A at a rate of 5 gal/s. There is a drain at the bottom of tank A. The solution leaves tank A via thi
Evaluate the following limit: Lim (100/x) x-> ∞
Please show me how to calculate the length of a curve. See attached file for full problem description.
Use the method of cylindrical shells to find the volume of the solid rotated about the line x=-1 given the condition: y=x3 - x2; y=0; x=0
Lim e^x x--> -∞
Evaluate log2 8
1. Compute the following limit: lim (x->2) [sqrt(6-x) - 2]/[sqrt(3-x) - 1] 2. Prove using the squeeze theorem lim (x->0) x^4 cos(2/x ) = 0 3. Show by means of an example that lim x-> a (f(x) + g(x)) may exist even though neither lim x-> a f(x) nor l
Determine the particular solution for the following nonhomogeneous differential equation using the method of variation of parameters Y" + y =tan(x); 0< x < pi/2 I got characteristic equation as y = U1 sin(x) + U2 cos (x) I was able to get thru to set the original D.E. to u'1 (x) cos (x) - u'2 (x) sin (x) = tan (x)
Find an equation of the line (in slope-intercept form) that passes through the points and sketch the graph of the equation. 1)(2,-1),(4,-1) 2)(-1,0),(6,2) write equations of the lines through the point parallel to the given line and perpendicular to the given line. 1)point:(3,-2) line:5x-4y=8 2)point:(-6,2) line:x=4
The relative decay rate of naturally occurring uranium U-238 was given in Example 4. Scientists estimate the age of the earth to be about 4.55 billion yr. Determine the fraction of the U-238 present when the earth was formed that is still present as U-238. EXAMPLE 4: A 1-G sample of pure uranium produces about 740,000 de