Initial value problem Definition and 172 Threads

Homework Statement Hello, I am wondering if someone can look at the following: suppose I'm given an initial value problem: dy/dt = ty(4-y)/3 with y(0) = a. So, if I separable the variables, i would get: dy/4(4-y) = t/3dt and I would get by partial fractions (1/4)*lny-(1/4)ln(4-y) =...

Homework Statement Solve the initial value problem for y. \frac{d^2y}{dx^2}\,=\,\frac{1}{a}\sqrt{1\,+\,\left(\frac{dy}{dx}\right)^2} y(0)\,=\,a & y\prime(0)\,=\,0 a is a non-zero constant. Homework Equations The calculus. The Attempt at a Solution y\prime\,=\,sinh\,x...

This question is an initial value problem for diffeq. We are asked to solve explicitly for y. (1+cos(x))dy = ((e^(-y))+1)*sin(x)dx , y(0) = 0 I attempted a separation of variables and ended up with the following: dy / ((e^(-y))+1) = (sin(x) / (1 + cos(x))) dx I know that my...

Homework Statement Solve the following initial-value problem \(y'+5y=1,\:y(1)=0\) The Attempt at a Solution y' + 5y = 0 (this is to solve for a general solution) y = -(5/2)y^2 -_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_ y' + 5y = 1 (this is for the particular solution) y = 1/5...

1.Solve the following initial value problem d^2y/dt^2 + 4y = { 1, 0<= t <=Pi/2 } {sin(t), Pi/2 < t} y(0) = 2 y'(0) = -1 I used y(t) = e^rt 3. For y'' + 4y' =1 y(t)= e^rt Yp(0)=1 r^2+4 = 0 r = 2i y1(t) = C1 Cos(2t) +...

I need some help with an initial value problem. It looked pretty easy at a glance, but I've ended up spending over 3 hours on this one problem.The problem is as follows: (e^(-y)+1)(sin(x) = (1+cos(x)) dy/dx With y(0) = 0. I rearranged the equation to get sin(x) / (1+cos(x)) dx = 1 /...

Homework Statement Given the below stated equations I need to find the exact polynomial given the initial condition. y(0) = 1 y = 4*t*sqrt(y) Homework EquationsThe Attempt at a Solution I simply disregard the initial value condition and get y = t^4 How can I find the fourth order...

Homework Statement a) Consider the initial value problem \frac{dA}{dt} = kA, A(0) = A_0 as the model for the decay of a radioactive substance. Show that in general the half-life T of the substance is T = -\frac{ln2}{k} b) Show that the solution of the initial-value problem in part a) can...

Homework Statement ********************************************** Find the two solutions of the initial value problem dy/dx = 3y^(2/3) ; y(0) = 0 The attempt at a solution ********************* I integrate to find the general solution y = (x + C)^3 c=0 is obviously a...

Solve the given initial value problem. 9y"-12y'+4y=0 y(0)=2 y'(0)=-1 9r^2-12r +4=0 (3r-2)^2 so r=2/3 so my general solution would be y(t)=c_1e^2/3t +c_2e^2/3t Whenever I try to use the initial conditions I can't get them to work. One disappears. Is my general...

milk containing 6% fat per gallon is pumped into a tank that initially contains 300 gal of milk at 3% fat. the rate at which the milk is pumped in is 3 gal per min, whereas the mixed liquid is pumped out at the same rate. a) find the number of gallons of fat in the tank at any time. b)...

i try to solce the initial value problem question and got f(x,y) = x^2 -x +y^2 +y +c and y(0)=2 is given how do i find c?? is it just make the eqn x^2 -x +y^2 +y +c = 0 and subs y=2 and x=0?? pls help thanx

Initial Value Problem I (kind of) understand how to do initial value problems. I know that if the problem is y' = x, y(4) = 3 then you just differentiate it, solve for y(4) and then replace the constant C (in the equation I differentiated) with this answer. But what if the initial value is...

I have a initial value problem that I have no idea how to start! Ahhh :( The equation is: xy' + 6y = 3xy^3 How do I start? I have no idea! ahhh :cry: I don't like DE's!

The equation starts with dy/dt = ay - b, and initial condition y(0) = y_o and y_o is an arbitrary value. The book says this can be rewritten as: (dy/dt)/[y - (b/a)] = a. But I don't see how do make that step algebraically. How can the original be rewritten like that? A problem at the end of...

The problem: The acceleration of a particle moving back and forth on a line is a = (d^2)s/d(t^2) = (pi)^2 cos(pi)(t) m/sec^2 for all t. If s = 0 and v = 8 m/sec when t = 0, find s when t = 1 sec. My work: (d^2)s/d(t^2) = (pi)^2 cos(pi)(t) ds/dt = (pi)^2 sin(pi)(1) + C ds/dt =...

i was taking my final today and came across an initial value problem. Seemed pretty simple, separate the variables, integrate, then use the initial value to find the value for the constantt C. The weird thing was that the constant C would be multipled by 0 when i plug in the given initial...

Consider the initial value problem y^{\prime} = \frac{3t^2}{3y^2 - 4} \mbox{,} \qquad y(1) = 0\mbox{.} (a) Use Euler's method with h=0.1 to obtain approximate values of the solution at t=1.2\mbox{, }1.4\mbox{, }1.6\mbox{, and } 1.8. (b) Repeat part (a) with h=0.05. (c) Compare the...

Hi I have to solve this equation using laplace transform ty''+(t-1)y'+y=t^2 y(0)=0 y'(0)=0 I tried it using MATLAB and get to this point (Int(-2/s^4*exp(1/2*s*(s+6)),s)+C1)*exp(-1/2*s*(s+6)) I think I've gone wrong somewhere Any Help would be appreciated. Thanks

\frac{dy}{dx}=x-4-xy-4y you are given that y(0)=4. so, here's what i did: \frac{dy}{dx}=(x-4)(y+1) \frac{dy}{y+1}=(x-4)dx i integrated both sides: ln(y+1)=\frac{x^2}{2}-4x+C y=e^{\frac{x^2}{2}}e^{-4x}e^{C}-1 plugged in for x and y: 4=e^{\frac{0^2}{x}}e^{-4*0}e^{C}-1 5=e^C...

Rewrite the differential equation \frac{dy}{dx}=x{\sqrt{y}} in the form y=f(x) given the initial condition f(3)=25. I am new to integration so I am unsure about my work on this problem. \frac{dy}{dx}=x{\sqrt{y}} dy=(dx)(x)(\sqrt{y}) \frac{dy}{\sqrt{y}}=(dx)(x)...

hi everyone. i need help solving this question ydx - (ytan(x/y) +x)dy = 0, where y(1) = pi/4 i know how to do the question but my problem is just i don't know how to get all the x's on one side and the y's on the other. any help would be appreciated. thanks a lot.