Initial Definition and 1000 Threads

Hey, We haven't properly covered this in class yet, but I am trying to study ahead using online course notes, I manage to finish a few questions but I have gotten stuck here, The question starts by asking for the solution to the ODE: y' = 1 - 2xy, When I solve this using the...

Homework Statement y''-4y'+4y=0 , y(1)=1 and y'(1)=1 The Attempt at a Solution Auxiliary equation: r2-4r+4=0 I tried factoring 2 different ways: (r-2)2=0 r=2,r=2 y1=e2t y2=y1 y(t)=c1e2t+c2e2t y(1)=c1e2+c2e2=1 ---eq(1)y'(t)=2c1e2t+2c2e2t ...c2=1/(2e2)-c1 ---eq(2) sub eq(2) into eq(1)...

Homework Statement In a particular star forming cloud the initial mass function (IMF) is given by N(M_{*})=Cexp(-M_*^2) where C is a normalisation constant. (The IMF describes the initial relative number of stars of different masses). Assuming that the number of hydrogen Lyman continuum...

Homework Statement Solve: dy/dy = y^3 given the initial condition y(0)=0 The Attempt at a Solution \int \frac{dy}{y^3} = \int dt \frac{-1}{2y^2} = t + c y^2 = \frac{-1}{2(t+c)} y = ± \sqrt{ \frac{1}{2(-t-c)}} This equation isn't going to support the initial condition, so can someone tell me...

Hi, I've got a problem here, that I'd like to discuss before trying to implement any sort of solution. Basically I've got a planetarium simulation, in which I'd like to plot a patched conic trajectory ahead of a spacecraft . The planetarium only simulates two-body gravity, and switches...

Homework Statement I had to calculate initial and final velocities for a rocket launch. Data are as follows: horiz displacement = 17.5m time = 3.5 s launch angle = 40 deg angle to apex from 20m = 11 deg net vertical displacement = 0 Homework Equations I used the following...

Given: Solve the initial value problem 2(√x)y'+y+4(√x) ; y(1)=2 I am having trouble separating the x's and y's in order to integrate. I keep coming up with: dy/dx +y/(2(√x))=2... What do I keep missing here? I am pretty sure you leave the y(1)=2 alone until you are finished with...

Homework Statement Solve the following differential equation with the given initial value y(0)=0Homework Equations 2sinxy dx + (x2 cos y - 1) dxThe Attempt at a Solution I am getting stuck trying to find the integrating factor

Homework Statement Solve the following Initial Value problem for x(t) and give the value of x(1) Homework Equations (dx/dt)-xt=-t , x(0)=2 The Attempt at a Solution (dx/dt)-xt = -t (dx/dt) = xt-t (dx/dt) = t(x-1) (1/(x-1)) (dx/dt) = t (1/(x-1)) dx = t dt Then I integrate...

Homework Statement Solve IVP y'' + 2y' + 2y = u_pi(t) + u_2pi(t) with IC y(0) = 0 and y'(0) = 1. Homework Equations L{f''(t)} = s^2Y(s) - sy(0) - y'(0) u_c(t) = u(t-c) -->Laplace--> e^-cs/s The Attempt at a Solution y'' + 2y' + 2y = u_pi(t) + u_2pi(t) y'' + 2y' + 2y...

Homework Statement Find the initial speed (Vo) in Projectile motion in terms of Gravity (g) Height (H) Range (R) Homework Equations Nothing has been given, however, have found these so far... Initial Velocity = sqrt((1/2 * g * R^2)/(cos2θ * (R * tanθ + H)) And a few others which are...

Homework Statement .019 Kg icecube @ unknown temperature (In deg C) Placed in 200 mL (.2 KG) water at 35 C. After melting, water is at 22.4 C. Find initial temperature of ice using conservation of energy. Homework Equations I've done the math a ton of times and keep getting -60 C...

I have the following ODE system \begin{cases} x' = v \\ v' = v - \frac{v^3}{3} - x \\ x(0) = x_0 \\ v(0) = 0 \end{cases} I am asked to find x_0>0 such that the solution (x(t),v(t)) is periodic. Also, I need to find the period T of such solution. I don't know how to solve the...

how can we solve this ODE? http://img818.imageshack.us/img818/3966/59962234.png

Thanks for clicking! So, I've got a problem here that I'm stuck on. I need to find the general solution to y' = (y3 + 6y2 + 9y)/9 I found this to be ln|y| + (3/(y+3)) - ln|y+3| = x + c but I would appreciate it if you would check my work. Anywho, once I have the general solution I...

y' = x x' = -5y-4x y(0) = 1 x(0) = 0 after finding the general solution as shown here http://www.wolframalpha.com/input/?i=y%27+%3D+x%2C+x%27+%3D+-5y-4x how do you go about applying the initial values and finding the complete solution?

Solve $\begin{aligned} & {{u}_{tt}}={{u}_{xx}},\text{ }x\in [0,1],\text{ }t>0, \\ & u(x,0)=f(x), \\ & {{u}_{t}}(x,0)=0,\text{ }u(0,t)=u(1,t)=0 \\ \end{aligned} $ where $f(x)$ is defined by $f(x)=x$ if $0\le x\le \dfrac12$ and $f(x)=1-x$ if $\dfrac12\le x\le1.$ I'm not sure how to...

Hi, I'm interresting about the weight of the support of the pendulum with an initial speed. It is the http://en.wikipedia.org/wiki/Pendulum but with an initial speed. The mass come at top with straight initial speed and after turn around the pendulum. I attempt to have the weight of the...

Homework Statement A ball with a mass of 1220 kg is moving in a straight line heading due east when it collides elastically with a second ball that is at rest. After the collision the first ball deflects 27.9 degrees north of its original path and the second ball moves in a line 62.1 degrees...

Determining Initial and Equilibrium Concentration (Help!) Homework Statement You are given the equation Fe3+ + SCN- -> FeSCN- You are performing an experiment in which you are mixing Fe(NO3)3 and NaSCN. A table is given and I will only list the first sets of data because if i can figure out...

Homework Statement A projectile of mass M kg is accelerated from rest to V m/s using a compressed air cannon. conceptually, we may consider the projectile to be a frictionless "piston" within a cylinder that is closed at one end and open to the atmosphere at the other end. Before firing...

Homework Statement A 100g of hot iron rivets is heated to some temperature and then quickly transferred to 120g of water at 40°C in a copper calorimeter of mass 50g and specific heat capacity of 400J/(kg.°C).It is found that the final temperature of the mixture is 100°C and the water has...

For a harmonic oscillator with mass M, spring of stiffness k and displacement the force equation is: -kx = Md2x/dt2 How do you handle the situation and work out a solution for x(t) when the mass has an initial velocity. E.g. a mass dropped onto the spring?

Homework Statement A cannon ball is fired horizontally off the top of a cliff that is 400 m high above the ocean. The ball hits the water 600 m away. With what speed does the cannon ball enter the water? Homework Equations I've tried using d_{x} = u_{x}*t d_{y} = u_{y}*t +...

Homework Statement 4y'' - 4y' + y = 0 y(1) = -4 y'(1) = 0 Homework Equations getting the coeff's gets messier and messier.. am i doing something wrong? The Attempt at a Solution 4y'' - 4y' + y = 0 y'' - y' - (1/4)y = 0 r_1 = r_2 = 1/2 general soln: y(t) = c_1e^(t/2) +...

L\frac{dI}{dt}+RI=E I(0) = I_{0} Where E is a constant. I know I need to separate the equation and integrate but I am not quite sure how given all the variables running around... I don't see how the condition of I(0) = I_{0} helps in any way.

The equation is y'' + 4y' + 4y = (3 + x)e-x and initial conditions y(0) = 2, y'(0)=5so from the associated homogenous equation I think the fundamental set of solutions is {e^-2x, xe^-2x} and so yc would be Yc = c1e-2x + c2xe-2x but now I don't know how to get Yp, particular solution or what...

I'm currently doing a Lab in my University Physics class to calculate the initial velocity of a ball right as it's fired from a cannon. I'm not particularly looking for the answers, just the equation needed (i think I copied the equation from the professor incorrectly). Here's what I have...

Homework Statement A 1.428 kg textbook is kicked 183 centimeters, what is the initial velocity right as it left the foot? Homework Equations fk-ma/W Vf^2=Vo^2*2aΔx The Attempt at a Solution We were given no time, no acceleration, and no force. I'm completely at a loss! this is what I have...

Homework Statement a golf ball is shot from a height of 6.5 ft above the ground at an angle of 45° above the horizontal. The ball lands 39 ft and 3 inches downfield. Assuming ideal projectile motion find: a. Initial velocity b. flight time c. maximum height Homework Equations r =...

I think my book is giving me the wrong answer...The problem is to find solution of following: r'(t) = t2\hat{i} + 5t\hat{j} + \hat{k} The initial condition is: r(1) = \hat{j} + 2\hat{k} My solution: r(t) = < (1/3)t3 + c1 , (5/2)t2 + c2 , t+c3 > r(1) = < 0 , 1 , 2 > r(1) = <...

I can do with just an equation, but if anyone is willing to help: Target is 25.6 m away from canon Initial Velocity = 16 m/s Time = 2.6 s Range = 26.7m No air resistance

I can do with just an equation, but if anyone is willing to help: Target is 25.6 m away from canon Initial Velocity = 16 m/s Time = 2.6 s Range = 26.7m No air resistance

I'm trying to understand a problem someone gave me recently. there is a frictionless track that initially starts flat then there is an incline of 20 degrees then it levels out again at the bottom of the incline. you have two masses, 1 is .4 kg and is located at the top of the hill and has an...

Homework Statement Determine the solution of the IVP y' + 4ty = 4t, y(0) = 6 Homework Equations The Attempt at a Solution p(t) = 4t g(t) = 4t μ(t) = e^{\int4tdt} = e^{\int p(t)} = e^{\int4tdt} = e^{2t^{2}} is this all I need? because i did \frac{d}{dt}(y * μ(t)) = p(t)...

dy/dt=t^(2)y^(3) , y(0)=-1 I need help solving this I put the integral (dy/y^3)= integral (t^2)dt but idk what to do after that or if that's even right

Homework Statement R(dQ/dt) + (1/C)Q = E_0 e^-t ...Q(0) = 0 and E_0 = a constant Homework Equations The Attempt at a Solution first i rearranged to give: Q' + (1/CR)Q = (E_0e^-t)/R next i multiplied all by integrating factor of: u(t) = e^integ:(1/CR) = e^(t/CR)...

Homework Statement A projectile returns to its original height after 4.08 seconds, during which time it travels 76.2 meters horizontally. If air resistance can be neglected, what was the projectile's initial speed? (Use g = 9.80 .) Homework Equations The Attempt at a Solution...

Two parallel plates are 2.0 cm apart and the electric field strength between them is 1.0 × 10^4 N/C. An electron is launched at a 45 degree angle from the positive plate. What is the maximum initial speed v0 the electron can have without hitting the negative plate? i think the answer is...

Homework Statement Solve the I.V.P. x2(dy/dx) = (4x2-x-2)/((x+1)(y+1)) , y(1)=1 Homework Equations The Attempt at a Solution So far, I got to this: y2/2 + y = log(x) + 2/x + 3log(x+1) + C I used the initial conditions to solve for C and got: C = -1/2 - 3log(2) Substituting C...

OK, so clearly I am missing something, because I know this is supposed to be a simple problem. It reads: solve the following initial value problem: dy/dt=-y+5 y(0)=y_naught my process is as follows: dy/(5-y)=dt integrate ln(5-y)=t+C exponential both sides 5-y=(e^t)(e^c)...

Homework Statement An arrow shot into the air has a time of flight of 6s and a range of 210 meters. Find the: A.) Initial Velocity and B.) The angle at which it was shot. Homework Equations none? The Attempt at a Solution I don't know how to solve this.

Homework Statement A student throws 0.22kg rock horizontally at 20.0m/s from 10.0m above the ground. Ignore air resistance. Find the initial kinetic energy of the rock Homework Equations Ek = mv^2/2 The Attempt at a Solution This sounds INCREDIBLY easy and every shape or form...

Homework Statement Rock A is thrown straight up from the top of a 25m tall building at a speed of 20m/s. Exactly 1 second later Rock B is thrown in such a way that it lands on the ground at the base of the building at the same instant that Rock A lands. What is the initial velocity for Rock...

Homework Statement I understand how to do initial value problems but I'm slightly stuck when the initial values are y(0) = y'(0)=0 The question is Solve: y''+3y''+2y=f(t), y(0)=y'(0)=0 where f(t) is a square wave. Homework Equations \Im{y'} =s\Im{y}-y(0)...

Homework Statement If sphere 2 were free to move its initial acceleration would be ___m/s^2 Homework Equations Two small spheres carrying charges q1 = 7.68 µC and q2 = 5.74 µC are separated by 19.9 cm. The mass of sphere 1 is 10.5 g and the mass of sphere 2 is 15.2 g. The Attempt at...

Homework Statement An applied force of 10.0N acts horizontally on a 0.50kg mass on a floor with the coefficient of friction being 0.40. If the object had an initial speed of 2.00 m/s, determine its speed at 15.0m. Homework Equations General Energy Conservation Formula Ek(i) + Ep (i) +...

Hey, I came across this question in my textbook, and there isn't an answer for it in the back, so I would just like to check if I have my head around it. The question is: 2 projectiles are launched at the same angle. Projectile 1 reaches a max height of twice that of the projectile 2. What...

Homework Statement A mass is hanging on a vertical spring, and oscillates in SHM with an amplitude of 10.0 cm, and period 0.500 s. The graph shows its motion as a function of time. At t = 0, the mass is found at x = -7.50 cm below the equilibrium position. Assuming that x(t) = A cos (ωt +...

I'm trying to solve a non-linear time-dependent diffusion equation to find R(x,t). To do so, I'm positing that : R(x,t)=\sum^{J}_{1}X_{i}(x)T_{i}(t) which allows me to arrive at something that looks like : dT_{i}/dt=A_{i}T_{i}(t)-B*T_{i}(t)^{2} The problem I'm having, through sheer...