Initial Definition and 1000 Threads

I need to find a solution to the following problem: (x^{2}-1)\frac{dy}{dx}+2y=(x+1)^{2} y(0)=0 I decided to try using variation of parameters. My teacher was unable to show any examples, and I'm having issues understanding the textbook. From what I see I need to get it onto this form...

A cannon sends a projectile towards a target a distance 1210 m away. The initial velocity makes an angle 26o with the horizontal. The target is hit. The acceleration of gravity is 9.8 m/s2 . What is the magnitude of the initial velocity? Answer in units of m/s y = viy•t +0.5•ay•t2 vix =...

Hi I need some help with this question: Estimate the maximum initial velocity you can achieve with a tennis ball I thought of using the maximum range formula: R=v2/g but doesn't that imply to the fact that I'm throwing at an angle of 45 degrees? Please help me, I really want to solve this...

How should I go about starting the following two problems solve the following initial value problems x''-4x=0 ; x(0)=1, x'(0)=0 and x''-4x'+4x=0 ; x(0)=1, x'(0)=0 Should i use a general solution with the basis m^2-4=0 for problem one and m^2-4x+4=0 for the second?

Hello all, I got this question off mastering physics and was unable to understand it. I eventually gave up to concentrate on other assignments and asked for the answer. I was unable to come up with more than one answer I thought possible without resorting to trial and error. Answer: Vx,Vy,Vz =...

Homework Statement Tow protons of equal energy collide head on and the result is p+p -----> p+p+ Pi0 If all particles produced at rest what must be the KE of the initial protons Homework Equations mass of Pi0 = 135MeV/c2 The Attempt at a Solution Total energy of the...

Hi can anyone help me with this formula: How do I end up with this equation, thanks in advance!

Homework Statement A juggler throws a ball just so it reaches the ceiling at 3.0 meters. (3m above hand) How do I solve for initial velocity? Homework Equations The Attempt at a Solution

How can you let Initial position and initioal velocity be equal to zero? I understand that it will be zero at time = 0, but as time goes on from 1, 2 , 3 , 4 won't it change? I underlined that it in read in the picture?

Homework Statement A flowerpot falls from the ledge of an apartment building. It takes .2 s for the pot to pass the 4 m window below. How far above the top of the window is the ledge from which the pot fell? (Neglect air resistance) Homework Equations y(t)=y0 + (voy)(t) - 1/2g(t^2)...

Ok so having a little problem with this one and i feel like its easier than what i am seeing, but just not sure how i can get a V-initial from this (Replaced actual numbers with AAA and BBB because i am trying to recall how to do all this, hope ya'll don't mind variables to much lol) The...

For the initial speed of an ideal projectile, how many launch angles equal for the range of the projectile -1 -2 -more than 2 but an infinite number of -only one if the angle is 45 but other wise only 2 -an infinite number

Homework Statement Gamma rays of energy 1.02 MeV are scattered from electrons that are initially at rest. If the scattering is symmetric, that is, if θ = ϕ in Fig. 1, find i. the scattering angle θ ii. the energy of the scattered photons. Homework Equations λ' - λ = (h/mc)[1 - cos(θ)] The...

Homework Statement If a flea can jump straight up to a height of .440 m, what is its initial speed as it leaves the ground? How long is it in the air? Homework Equations x = (1/2)at^2+Vo+xo V + at+Vo V^2 = Vo^2+2a(delta x) x-xo = ((Vo-V)/2)t It has to be one of these, since that's...

Initial angular momentum = 0 when we fall from a height, how does our head automatically reach the ground first than our legs though the initial angular momentum is zero?

Homework Statement Two identical small metal spheres with q1 > 0 and |q1| > |q2| attract each other with a force of magnitude 70.2 mN, as shown. The spheres are then brought together until they are touching. At this point, the spheres are in electrical contact so that the charges...

Homework Statement Find the solution to the initial value problem dy/dx - y = e^3x y(0) = 3 Homework Equations e^∫p(x) The Attempt at a Solution Do I treat p(x) = -1? I(x) = e^∫-1 = e^-x e^-x(dy/dx) - ye^-x = e^3x . e^-x e^-x(dy/dx) - e^-x . y = e^2x e^-x . y = ∫e^2x y = (2e^2x...

Homework Statement Suppose that I am jumping on the Earth, and I weigh 130 lbs. I push off with an initial vertical velocity of 2 m/s, and reach my highest height at 4 m. If I were to jump on a different planet with an extra 130 lbs (earth weight) because of a space suit etc., would I have a...

Homework Statement 1. Find he solution of the initial value problem: x^2 (dy)/(dx) = 4y y(1)=2 2. Find the general solution of the differential equation: (dy)/(dx) - 2y = e^(5x) The Attempt at a Solution i'm completely confused by this, no idea where to start. If...

Homework Statement The position x of an object as a function of time is given as x = 2.257 + 4.894 t + 16.5 t2. All quantities are understood to be quoted in SI units. What is the initial velocity ? Indicate with a negative (positive) sign whether the acceleration is constant (not constant)...

Homework Statement http://scc.scdsb.edu.on.ca/Students/onlinecourses/Sikora/sch4u/v12/64.pdf That is the lab I have been working on. I've done the lab but I am answering the questions. I don't understand the Analysis question #1. How do I calculate the reaction rate for oxygen if I don't have...

Driving along a crowded freeway, you notice that it takes a time t to go from one mile marker to the next. When you increase your speed by 4.5 mi/h, the time to go one mile decreases by 9 s. What was your original speed? I've been working on this for 2 hours, I can't seem to get the formula...

theorem states that for y'' + p(x)y' + q(x)y = r(x); if y1 & y2 are random numbers such that y(m) = y1 and y'(m) = y2 then we can find a unique solution y for above differential equation... in y'' - y'/x = 0; both y = x^2 and y = 0 and y = k x^2 satisfy above with .. y(0) = 0; and...

Homework Statement At time t = 0, a car has a velocity of 16 m/s. It slows down w/an acceleration given by -0.50t in m/s^2 for t in seconds. It stops at t =? Homework Equations The Attempt at a Solution v = 16 - 0.5t 16/.5 = t 16 x 2 = t 32 = t Did I set this up wrong? My...

Homework Statement The "hang time" of a punt is measured to be 3.50 s. If the ball was kicked at an angle of 69.0° above the horizontal and was caught at the same level from which it was kicked, what was its initial speed? (Neglect air resistance.) Homework Equations All Kinematics...

Homework Statement Solve the Initial value problem using Laplace transform \ddot{y} +2y = 0, y0 = C1, \dot{y} = C2 Homework Equations [s2 - sy(0) - y'(0)] + a[sY - y(0)] + bY The Attempt at a Solution s2Y - sy(0) - y'(0) + 2y = 0 s2Y + 2Y = sy(0) + y'(0) (s2 + 2)Y = s(C1) + (C2)...

Homework Statement sin(y)\frac{ \partial u}{ \partial x} + \frac{ \partial u}{ \partial y} = (xcos(y)-sin^2(y))u where ln(u(x,\frac{\pi}{2})) = x^2 + x - \frac{\pi}{2} for -1 \leq x \leq 3 determine the characteristic curves in the xy plane and draw 3 of them determine the general...

Hi, I need to calculate the magnitude of the initial velocity of the following data for projectile motion. Any help would be greatly appreciated as I have no idea where to start! Thanks please see the question here: http://i52.tinypic.com/15p0kza.png and the data here...

Hi, I need to calculate the magnitude of the initial velocity of the following data for projectile motion. Any help would be greatly appreciated as I have no idea where to start! Thanks please see the question here: http://i52.tinypic.com/15p0kza.png and the data here...

Do you have to pay for wi-fi, or for monthly fees or anything with an i-touch?

Hello experts! As we know that there are 3 different general solutions of an ordinary differential equation depends on that what type of roots we've gotten in the solution, listed below. 1) y(t)=c1em1t+c2em2t 2) y(t)=c1emt+c2temt 3) y(t)=c1eucos(v)+c2sin(v) Now 1st solution is used...

So the question is y" - y' - 6y = e^-x + 12x, y(0)=1,y'(0)=-2 First I found the general solution which came out to be, Ae^3x + Be^-2x I then Substituted y=ae^-x + bx + c y'=-ae^-x + b y"=ae^-x Then I just compared the coefficients to get a=-1/4, B=-2 and C=-1/6 So I am getting y =...

a 3rd order IVP I am havin trouble with: y''' -3y'' +2y' = t + e^t y(0)=1, y'(0)= -.25 y''(0)= -1.5 I am using At^2 and B*e^t *t as my Y1 and Y2. Is this correct?

hi there, i'm programming a simulation of a projectile that has a known target off in the distance somewhere in my 3D world, i also know the angle at which i will be firing the projectile. i am firing the projectile on flat ground (so the start and end y-coordinates are the same). i'm...

Hey folks, I have an orbit in the circular restricted three body problem with initial conditions [x(0), 0, z(0), 0, y'(0), 0] I'm following this paper http://adsabs.harvard.edu/full/1984CeMec..32...53H on how to correct these initial conditions given the state transition matrix at a...

One particle has a mass of 3.00 10-3 kg and a charge of +7.50 µC. A second particle has a mass of 6.00 10-3 kg and the same charge. The two particles are initially held in place and then released. The particles fly apart, and when the separation between them is 0.100 m, the speed of the 3.00...

Homework Statement In a baseball game, a batter hits the ball at a height of 4.60 ft above the ground so that its angle of projection is 52.0º to the horizontal. The ball lands on the grandstand, 39.0 ft up from the bottom. The grandstand seats slope upward at 28.0º with the bottom seats 358...

Hey folks I'm looking into halo orbits and I have a question about how to find the initial conditions from the third order approximation solution... A good run through of the third order solution calculation is found in this paper...

Hey, we have to solve the following problem for our ODE class. Homework Statement Find the solution of the initial value problem dx/dt = (x^2 + t*x - t^2)/t^2 with t≠0 , x(t_0) = x_0 Describe the (maximal) domain of definition of the solution. The Attempt at a Solution Well...

1. y'' -5y' + 6y = 0, y(0) = 1, y'(0) =2 3. [s^2 F(s) - s f(0) - f'(0)] -5 [F(s) - f(0)] + 6[F(s)] = 0 (s^2 +1)F(s) - (s -5)f(0) - f'(0) = 0 (s^2 + 1)F(s) - (s-5)(1) - 2 = 0 (s^2 + 1)F(s) = s -3 F(s) = (s-3)/(s^2 + 1) Here's where I'm stuck. I can't factor the denominator to...

I am having trouble with the below problem: y'-(3/2)y= 3t+ 2e^t, y(0)= y0. fine value of y0 that separate solutions that grow positively and negatively as t=> infinity. I found p(t) to be -3/2, u(t) to be e^-3t/2 => e^-3t/2*y' - 3y/2( e^-3t/2)= e^-3t/2(3t+ 2e^t) => -2 -4e^t + ce^...

I need help with an initial value problem, ty' + (t+1)y= t; y (LN 2)= 1 I divided t and have u(t) as exp Integral of t+1/1 => e^t +t Multiplied this to the original equation to get (e^t +t)y' + ((t+ 1)/t) *y *(e^t +t) = (e^t +t) How can I integrate the above? Are my steps so far...

Homework Statement Proof that there exist more than one solution to following equation \frac{dx}{dt} = \sqrt[3]{x^{2}} , x(0) = 0Homework Equations The Attempt at a Solution Well, I need a confirmation to my attempt of solution. The one is quite forward: \Rightarrow x=(1/3(t+c))^{3} Pluging...

A ball is thrown into the air from ground level. After a time t = 2 s, the ball has traveled to a position x1 = 27 m to the right of and y1 = 10 m up from where it was thrown (at this time, the x and y components of the ball's velocity are still positive). The axes show the x and y directions to...

Homework Statement Find the general solution for the following systems of equations, a solution to the initial value problem and plot the phase portrait. --> this is in matrix formx' = 1 2 0 3 all multiplied by x. also, x(0) = 2 -1 Homework Equations Determinant, etc.The Attempt at...

Discern initial V w/o components!? Homework Statement Ok, ball traveled 188m (618 ft) before landing on the ground. Assume ground is flat, and ball Vi is from 45o, disregard air resistance, and Starting position is .9m above ground. Find Vi I KNOW )))) a= 9.8 m/s2...

Homework Statement I'm having trouble finding the initial velocity without knowing the time. A basketball player is standing on the floor 10.0 m from the basket. The height of the basket is H = 3.05 m, and he shoots the ball at an angle, θ = 42.0°, with the horizontal from a height of h =...

Homework Statement A ball ( 2.7 g ) is launched at a 45 degree angle with a solenoid input of 50V. What is the initial speed of the ball? Homework Equations KE = 0.5mv^2 PE = mgh dy = vy(0)t + 0.5at^2 dx = vx(0)t The Attempt at a Solution Voltage is potential energy and I...

Is this problem possible? Solve the initial value problem x''(t) + 6x'(t) + 9x(t) = f(t); x(0) = N, x'(0) = M I get to X(s)=(F(t)+Ns+6N+M)/(s^2+15) and don't know where to go from here. Any help would be appreciated.

Homework Statement A ball with mass m = 1.72 kg is attached to a peg at the origin using a length of massless string of L = 1.54 m. It is released from the top of a vertical circle with speed v0 = 4.81 m/s. What is the ball’s speed (m/s) when the string makes an angle θ = 21.7° above the...