Initial Definition and 1000 Threads

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...

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 +...

Eq u'(x)+p(x)u=f(x) with initial condition u(0)=0 It's homogenous solution is u_h=Ce^{-\int^x_0 p(s)ds} Complete solution u(x)=e^{-\int^x_0 p(s)ds}\int^x_0f(s)e^{\int^s_0 p(z)dz}ds=\int^x_0 f(s)g(x,s)ds where g(x,s)=e^{-\int^{x}_s p(\xi)d \xi } I didn't see that last...

Hi, I was wondering if someone could point me to a textbook or easy to read paper (or website) that briefly describes/proves the differences here. What I mean is if I do classical (continuous energies) statistical mechanics where my initial state is a volume (greater than or equal to h-bar)...

Homework Statement A spherical billiard ball radius a and mass M is sitting on a flat surface. The coefficient of friction between the ball and table is u. The moment of inertia for the billiard ball is 2Ma^2/5. The ball is given a sharp horizontal hit at the centre and it starts moving with...

Homework Statement Show that R_{00}= -\frac{1}{2}g^{\alpha\beta}g_{\alpha\beta,00}+ M_{00}, where M can be expressed solely in terms of the initial data, which is the metric tensor and its first derivatives. Homework Equations R_{ab}= R^c_{acb}= \Gamma^a_{bd,c}- \Gamma^a_{bc,d} in...

Homework Statement We know that y = Aex is the solution to the initial value problem dy/dx = y; y(0) = A. This can be shown by solving the equation directly. The goal of this problem is to reach the same conclusion using power series. Method: Let y be a solution to the initial value...

I need help to solve this problem: The initial mass function (IMF) of main-sequence stars, n(M) follows a shape called the Salpeter function,which is described by n(M)=kM^-2.35, where k is a normalising constant and M is the stellar mass in solar masses. The IMF is similar in some sense to a...

Homework Statement I need to find Vi, knowing the following: Δt=6/Vi cos40 Viy=Vi sin40 Δy=4m ay=-g = -9.8m/s^2Homework Equations Quadratic: x= [-b +/- √(b^2-4ac)]/2a Kinematic equation to be used: Δy=ViyΔt + 1/2ayΔt^2The Attempt at a Solution Δy=ViyΔt + 1/2ayΔt^2 4=(Vi sin40)(6/Vi...

How to find the initial velocity required for a projectile to be launched at an angle theta, with a distance 'd' and height 'h'. An expression is required. I am unable to find one using all three. Thanks in advance.

[b]1. A fixed amount of gas initially at 100 K and pressure P1 is expanded from 1 L to 100 L in a piston. The temperature, T2, of the gas at this point is 50 K. The piston is then locked at constant volume V2=100 L and half the gas is pumped out at a constant temperature of T2 . The observed...

Homework Statement An ice-water mixture has a mass of 180g and is contained in a 100g aluminum calorimeter When 35g of steam at 100 degree Celsius is condensed in the water, the temperature rises to 50 degree Celsius. How much ice was in the container initially? The heat capacity of water is...

HI all There is smth I don't understand in building initial data for BH The equations everybody uses uses spacetime or timelike hypersurfaces but for example horizon is a null surface!

Homework Statement A 10 g ball going at a speed of 5 m/s is kicked, and flies off at an angle of 35° at 25 m/s. What was the force of kick? Known: m = 0.0010 kg vi = 5 m/s θ = 35° vf = 25 m/s Homework Equations mvi = mvf F = ma The Attempt at a Solution Would this count as an...

So, let's assume the switch has been closed for a long time. The capacitor is charged to 12V, and the coil acts like a short-circuit. Immediately after opening the switch, is it right to say the Voltage in the coil is 12V? My notes specify something along the lines of: the conditions at time...

Is there any way to mathematically derive functions that satisfy a given set of initial conditions? I know this sounds very general, but say for: f(1)-f(0)=0 and f'(1)=1 I've resolved myself to guessing and checking. I've found a function for the opposite: e*t-exp(t) -- ([e*1 -...

This problem has been bothering me for a while now, hope you can help me. Let's say that the initial velocity of an object, with mass of m is 0 and the initial position is s0 and the force acting on the object is defined as F(s), how do i find the s(t), where t is time. If it's any help, then...

Given: Mass= 5 kg Vo= 40 m/s Vf=50 m/s s=150 m Ho=0 Hf=50.2 m g=9.8 m/s/s friction=6.26 N θ=30° *You will probably not use all of these values* What percent of initial total mechanical energy is lost during the round trip? (a block (with mass m) going up an inclined plane, and...