Diff eq Definition and 271 Threads

Homework Statement Find the solution for y"+2y'+5y=(e^x)sinx Homework Equations The Attempt at a Solution So far I think I've gotten the solution from the characteristic equation, but I'm having trouble with the particular solution. For the characteristic equation solution...

Homework Statement Solve the initial value problem: \frac{dy}{dt} + 2y = u_2(t)e^{-t} y(0) = 3 Where u_2(t) is a Heaviside Function with the discontinuity at t=2. Homework Equations The Laplace transform of a Heaviside function multiplied by another function: L( u_a(t)f((t-a) ) =...

I have run into this problem solving differential equations of this type (they occur often doing momentum problems): kxy = (y+dx)(x+dy) where k is constant. I multiply it out to : kxy= xy + xdx + ydy + dydx Regroup and : [tex] \int {kxy} = \int {xdx} + \int {ydy} + \int {dydx} [/itex]...

Homework Statement Calculate ZIR(t) for the system described for the following differential equation, where the initial condition is y(0-) = 5: Homework Equations 2y' + 3y = 2x' + x(t-1) The Attempt at a Solution I'm pretty sure we're supposed to laplace-transform it, then find Y/X...

Homework Statement Find the exact solution to this problem y'=4x–y+9;y(0)=6 The Attempt at a Solution I am panicing because I have an exam tomorrow and I can't remeber a lot of the basics for diff eq. I tried to solve this using 2nd order style... first I made it y'-y=4x+9...

Here's the problem: x^2y''-3xy'-12y=0 with initial conditions y(1)=0 and y'(1)=7 I'm supposed to solve for y in the form y=c1y1+c2y2 y1 = x^6 by inspection Now to solve for y2 y2=y1v v can be solved for by the equation y1v''+(2y1'+py1)v'=0 where p is the function in front...

Crap, nevermind, I left b^2 out of the quadratic formula, thanks anyways. Here's the question: Find y as a function of t from the diff eq: y''+6y'+25y=0 with the initial conditions y(0)=8 and y'(0)=8 I used the form r^2+6r+25=0 to solve for r and through the quadratic equation got r =...

Never mind, I figured it out. Here's the question: Find the general solution to the homogeneous differential equation https://webwork.math.uga.edu/webwork2_files/tmp/equations/59/540a7a16e5c4e841a098d9d2a72f0a1.png The solution has the form...

I have two coupled harmonic oscillators: \ddot{x}_{1} = -2kx_{1} + kx_{2} + f(t) \ddot{x}_{2} = kx_{1} - kx_{2} Mass 1 is at position x_{1} and subject to force f(t). I take the Laplacian of the first equation and solve for X_{1} to get X_{1} = \frac{ F(p) + k X_{2} }{ p^{2} + 2k }...

I have a logistic issue with differential equations. I have spent four hours working on this problem and it is way past the point of ridiculous. If anyone can help out that would be great. It begins like this. dy/dt = k(P-y)*y. It is an epidemic model, where k is a positive constant...

Ok, so i tried to solve this problem: Find y as a function of t if: 100Y"-729y=0; y(0)=6, y'(0)=1 this is what i did so far: 100r^2-729r=0 r(100r-729)=0 r=0, r=729/100 y(x)=C1+C2*e^((729/100)*t) y'(x)=C1+729/100C2*e^((729/100)t) am I on the correct track? After I substitute the...

this is from a Diff EQ but but its just algebra i think?? I'm just working through an example here and its say to solve the equation (y/k)=(ynot/k)/((ynot/k)-[1(ynot/k]e^(-rt)) for t. then in the next line it shows it solved for e^(-rt)={(ynot/k)(1-(y/k)}/{(y/k)(1-(ynot/k)} now i have...

(s+1)/s*(s^2+s+1) find laplace transform.. i am confused how to solve this problem i did numerator separation and i did A/s + (Bs+c)/(s^2+s+1) but still doenst work..so experts..i do really need ur help..thnx in advance

Any hints to this problem? "Assume the solution to a differential equation is given by \frac{dy(x)}{dx}+ay(x) = f(x) where y(0)=y_0 and a is a constant. Show how y(x) can be written as a convolution of f(x) and an exponential e^{ax}." The only hint we got from the prof was to multiply...

Hey, So I solved this one linear DE and the answer I got isn't the same as the one in the back of my textbook... And I'm not sure why. I thought I was doing this right. Could someone tell me what I'm doing wrong? Here's what I'm given: x^{2}y'+xy=1...

hi guys..i got a problem while doing my diff eq assignment:confused: hope u guys can give me hand..any help ll be appriciated Obtain the solution of the diff eq.. x' + ax = A sinωt x(0)= b thnx guys..

I took an ODE course last year, but I seem to have forgotten some stuff. I need to solve this equation: \frac{d^2u}{dt^2} + {\omega}^2u = f_osin({\mu}t) with the boundry conditions: u(0) = 0, du/dt(0) = 0 When I tried to solve the homogenenous equation first, I got...

Draw a direction field for the given differential equation. Based on the the direction field, determine the behavior of y at t goes to infinity. If this behavior depends on the initial value of y at t=0, describe the dependency. y'= -1-2y In class we did examples where we had a range...

Suppose a tank containing a liquid has an outlet near the bottom. The velocity of the liquid flowing out of the outlet is equal to a particle free falling without drag. a. show that v=sqrt(2gh) b. by finding the rate of outflow to the rate of change of the liquid in the tank, find...

diff eq of mechanical system w/ friction with zero input... I was wondering how we get around modeling mechanical systems with frictional forces (forces proportional to normal force and in the direction opposite of the motion) and the external force is zero. So, take for example a second order...

I have just started my first diff eq class, and I am struggling with the concepts. In the section 'Preliminary Theory' we are given Picard's Theorem and a few odd examples. Then this is the question from the homework: "Determine a region of the xy-plane for which the given differential...

I just need a hint or something to see where I start. I'm at a loss for a beginning. Consider the non-homogenous equation y'' + xy' + y = x^2 +2x +1 Find the power series solution about x=0 of the equation and express your answer in the form: y=a_0 y_1 + a_1 y_2 + y_p where a_0 and...

I am working on a Differential Equation problem and I am stuck on these two integrals: http://forums.cramster.com/Answer-Board/Image/cramster-equation-20064101738436328028752372062504976.gif and...

I'm looking for any resources you guys can point me to on "real" applications for differential equations. I have a relatively decent grasp of the math, but it's very frustrating for me learning sterile math with no idea what it's used for, especially since I figure that I'm going to actually...

Hello everyone. I'm going back to all my old webworks and trying to finish them and I'm still having problems on first order. It says this is seperable but I'm not seeing it. Here are the directions: The differential equation...

Hello everyone! I remember doing these in calc II, but forgot 99% of it. Here is the question: Find the interval of convergence for the given power series. http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/5e/119a4cd07ce5d3f6f673477ed169641.png The series is convergent from x = ...

ello ello! I havn't seen an example of this type of problem. It has another variabler in the equation, i tried to divide by it, but its still in there. Here is the problem: Find y as a function of x if...

Hello everyone! its me! I thought i for sure did this one right, but no, lies! Directions are to find a particular solution Here is what i did: http://suprfile.com/src/1/1t3y9m/lastscan.jpg Thanks :)

Ello ello! I'm looking at an example problem my professor did which is very similar to the one that i am doing, the only difference is his problem is: y''+y = sin(t) mine is: y''+9y = 6sin(3t); THe problem says: Find a particular solution to y'' + 9 y = 6sin(3 t) . y_{p} = so here is what i...

OKay everyone, this is a big f'ing problem (to me anyways) and its only worth 1 point! But I'm doing it anyways. So here was my attempt, everything seems to be working out like it should but look at what u1 came out too, what am i going to do with that mess? Also do u see any mistakes...

Hello everyone! i'm confused on how to approach this problem, my professor did an example and he used m^2-m-4m+6 = 0, if u have t^2*y''-4ty' +6y = 0; So i tried to do the following, but the answer is wrong. Anyone see? http://img88.imageshack.us/img88/3603/lastscan7jj.jpg THanks!

Varation of Parameters fun! diff EQ question, where do i go next? This is my first attempt at doing Variation of parameters, didn't go to bad, things cancled out pretty well but now I'm almost done but I'm stuck! The problem says: Find the solution of y''+15y'+56y = 54*e^(-5t), with y(0) = 8...

Hello everyone, I'm slightly confused on this problem, when i factored it and solved for r, i came out with only 1 answer, r = -13/72 Here is my problem and work: http://img213.imageshack.us/img213/685/lastscan15uk.jpg :biggrin:

intro to DIFF EQ (help!) a drag chute must be designed to reduce the speed of a 3000-lb dragster from 220 mph to 50 mph in 4 sec. Assume that the drag force is proportional to the velocity. a) what value of the drag coefficient k is needed to accomplish this? b) how far will the dragster...

OKay i havn't gotten 1 2nd order Diff EQ right yet! I'm on a role! wee! Find y as a function of t if 81y'' + 126y' + 79y = 0, y(0) = 2, y'(0) = 9 . Here is my work: http://img204.imageshack.us/img204/4605/lastscan5ag.jpg I submitted this and it was wrong...

Hello everyone. I"m not getting this problem right. <insert sad face here> Find y as a function of t if 6y'' + 33y = 0, y(0) = 8, y'(0) = 5 . y(t) = hokay, here is my work, it is sloppy sorry. Can you see any obvious mistakes I made? Note: the sqraure root should be encompassing both the 11...

Hello everyone, we just started 2nd order differentials, and i was loooking at his example and it made senes but now I'm doing the homework and I'm stuck. Here is the problem: Find y as a function of t if y'' - 3y' = 0, y(0) = 9, y(1) = 7 . y(t) =? Well there is my work...

Hello everyone. This problem has 4 parts. I got part (a) which is suppose to be the hardest part but I'm confused on how to (b) Plot Qn(t) for n = 1...4 observe wether the iterates seem to be converging. Well this is the series solution I got for the differential equation...

Hello everyone. We just started working with exact equations and I'm confused on what I do next! here is the problem: Use the "mixed partials" check to see if the following differential equation is exact. If it is exact find a function F(x,y) whose level curves are solutions to the...

Hello everyone I'm stuck on this problem: http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/18/0c06a4e72ea888ea65443a46afd42f1.png http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/90/dff750d2ab4fefb41eccca8ce709a01.png Looks simple enough but the answer they said is wrong. Here...

more Diff EQ fun! http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/58/6217226076d5fd259f53ad1e3ed4071.png Find such a solution and then give the related functions requested. http://cwcsrv11.cwc.psu.edu/webwork2_files/tmp/equations/57/f15a6cea760ce4906a6ec16f9d29451.png I submitted...

Hello everyone the problem I am messing up is: . Solve the following initial value problem: http://img59.imageshack.us/img59/9037/lastscan4vl.jpg When pluggin in answers and using my calculator to evaluate, its saying NON-REAL numbers, I'm messing up hardcore somewhere but not sure where...

Hello everyone. I don't see how this problem is wrong, i never do. Here it is: Solve the differential equation (y^{15} x ){dy}/{dx} = 1 + x. Use the initial condition y(1) = 3. Express y^{16} in terms of x. y^{16} = ? y^15*dy = (1+x)/x dx; I integrated both sides and got: (y^16)/16 =...

Its me again! I'm just having a full day of Diff EQ! 90% of the time I'm wrong but I'm learning slowly! but here is another problem: The directions say: Find the particular solution of the differential equation \frac{dy}{dx} + 5 y = 7 satisfying the initial condition y(0)=0. Answer: y = ? I...

I'm lost on this one, i checked my problem over a few times and i don't see any algebraic errors, did i break some rule? Thanks! :smile: Find the solution of the differential equation (ln(y))^4*{dy}/{dx} = x^4 y which satisfies the initial condition y(1)=e^2. y= ? Here is my work...

Hello everyone this may be an easy problem, but I'm confused on what they have given me the problem says: Find f(x) if y = f(x) satisfies {dy}/{dx} = 32 yx^{15} and the y-intercept of the curve y = f(x) is 2. f(x) = ? But what does that mean that the y intercept is 2? is that an...

Hello everyone i did this one surley thing it would work out and yet another failure. :cry: Solve the separable differential equation 11 x - 8 y*sqrt{x^2 + 1}*{dy}/{dx} = 0. Subject to the initial condition: y(0) = 6. y = ?I'm pretty sure where I messed up is when i tried to solve for y, i...

Hello everyone I'm stuck, i got right to the end of this intial value problem and it doens't seem to want to work. Solve the separable differential equation for u {du}/{dt} = e^{3 u + 10 t}. Use the following initial condition: u(0) = 6. u = ? I might have screwed up here: du =...

Hello everyone I'm lost on how they want me to approach this: Find the two values of k for which y(x) = e^{kx} is a solution of the differential equation y'' - 16 y' + 60 y = 0. smaller value =? larger value = ? I did the following: y(x) = e^(kx); y' = ke^(kx); y'' = k^2e^(kx)...

A body moving with velocity V enounters a resistance in the form of dV/dT=-k*V^(3/2). Show that V(t)=(4v.)/(k*t*sqrt(v.)+2)^2 v. is the same as v(subscript 0) When i solve the differential equation i keep getting V(t)=4/(k*t-v')^2 I have no idea how to get from dv/dt to the given v(t)