2nd order Definition and 464 Threads

This isn't really an exact homework problem since it's for a report I'm doing. Basically, I was wondering what the design for a second order passive low pass filter looks like. I know how to design a regular first order circuit but I have no clue about a second-order PASSIVE LPF. I tried...

Homework Statement y''-2ay'+a^2y=e^ax Find a general solution 2. The attempt at a solution I've found the general solution of the homogeneous eq: Ce^ax+Dxe^ax Next, I must find a particular solution on the form Be^ax (*), right? The derivative of (*) is Bae^ax and the 2nd...

Homework Statement Solve the initial value problem u\prime\prime+u=0.5cos (0.8t)\\ u(0)=0 \ u\prime(0) = 0 Homework Equations u(t) = [A*cos (w_nt)+ B*sin (w_nt)] + \frac{F_0}{m(w^2_n-w^2)} \left\{\begin{array}{cl} sin(wt)\\ cos(wt) \end{array}\right. The Attempt...

Homework Statement How do I go about solving d^2\theta/dt^2+ (g/L) \theta= g? It's been 2.5 years since I had diff eq. Homework Equations ^ The Attempt at a Solution I don't know. I've spent the past 2 hours going through old books and searching online and still can't figure it out :frown:

Homework Statement the equation of motion for a damped harmonic oscillator is d^2x/dt^2 + 2(gamma)dx/dt +[(omega0)^2]x =0 ... show that x(t) = Ae^(mt) + Be^(pt) where m= -(gamma) + [(gamma)^2 - (omega0)^2 ]^1/2 p =-(gamma) - [(gamma)^2 - (omega0)^2 ]^1/2 If x=x0 and...

Homework Statement If y = (3x)/e^2x, find the value of x when d^2y/dx^2 = 0 Homework Equations I'll just abbv d^2y/dx^2 as d2ydx2 The Attempt at a Solution I kept getting stuck at: d2ydx2 = 6/e^2 When d2ydx2 = 0, 6/e^2 = 0 6 = e^2 Then where's my x?? :confused: :confused...

Homework Statement y''+4y=t^2+3e^t y(0)=0 y'(0)=2 Homework Equations CE: r^2+4 r=+/-2i gs: y=c1 cos(2t) + c2 sin(2t) The Attempt at a Solution guess: yp=(At^2+Bt+C)e^t yp'=At^2e^t+2Ate^t+Bte^t+Be^t+Ce^t yp''=At^2e^t+4Ate^t+Bte^t+2Ae^t+2Be^t+Ce^t back into problem...

(a) Let alpha (a) and beta (b) be given constant. show that t^r is a solution of the Euler equation t^2 d^2y/dt^2 + at dy/dt + by = 0 , t>0 if r^2 + (a-1)r + b = 0 (b) suppose that (a-t)^2 = 4b. Show that (ln t)t^(1-a)/2 is a second solution of Euler's equation. please help, i have no idea...

Given that the equation t d^2y/dt^2 - (1+3t) dy/dt + 3y = 0. has a solution of the form e^ct, for some constant c, find the general solution (The answer is y(t) = c1(1+3t) + c2e^(3t) Edit: I finished this question as i figured it out. but when i come down to the last step, i get this y1(t) =...

differential equations - 2nd order homogenous eq'n sorry the title should read 2nd order homogenous eq'n, not nonhomogenous Find the general solution of the equation: (1+t^2)d^2y/dt^2 - 2t dy/dt + 2y = 0, given that y1(t) = t is one solution. My attempt: divided equation by 1+t^2...

Homework Statement Consider y'' = - sin(y) find a conserved quantity for this equation Homework Equations This looks an awful lot like a simplified version of a nonlinear pendulum equation The Attempt at a Solution For a conserved quantity I guessed: E = -cos(y) + y' because...

Homework Statement Suppose that u(t) is a solution to y'' + p(t)y' + q(t)y = 0 Suppose a second solution has the form y(t) = m(t)u(t) where m(t) is an unknown function of t. Derive a first order linear differential equation for m'(t). Suppose y(t) = e^(2t). Use the method...

Homework Statement Given: y'' - y - (y^3) = 0 (equation 1) E = (1/2)(v^2) - (1/2)(y^2) - (1/4)(y^4) (equation 2) v = y' i. Show that E is a conserved quanitity ii. Find all the solutions with E = 0 2. The attempt at a solution I'm not sure how to show a...

Consider the equation 2t^2y'' + 3ty' - y = 0 (a) Show that y1(t) = sqrt(t) and y2(t) = 1/t are soltuions of the equation on the interval 0<t<infinity (b) Compute W[y1,y2](t). What happens as t approaches zero? (c) Show that y1(t) and y2(t) form a fundamental set of solutions of the equation...

Homework Statement y'' - 4y = 0 when y = 1, y' = -1, x = 0 2. The attempt at a solution y'' - 4y = 0 m^2 - 4 = 0 m = 2, m = -2 Substituting: y = 1, x = 0 1 = C1 + C2 C1 = -C2 + 1 Substituting: y' = -1, x = 0 -1 -C2 + 1 + C2 C2 = C2 Therefore: y = -C2e^2^x +...

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 am currently solving a physics problem that requires me to solve the following equation m(d^2x/dt)=-gamma-c(dx/dt) but I can't seem to come up with a method that makes sense. Note: Gamma is just some constant. I tried to integrate both sides wrt t but then I end up with both a velocity...

Homework Statement The homogeneous Helmholtz equation \bigtriangledown^2\psi+\lambda^2\psi=0 has eigenvalues \lambda^2_i and eigenfunctions \psi_i. Show that the corresponding Green's function that satisfies \bigtriangledown^2 G(\vec{r}_1, \vec{r}_2)+\lambda^2 G(\vec{r}_1...

Let's say that I solve a inhomogeneous differential equation of the type d2y/dx2+k*dy/dx = g (k and g being constants) ..and I get the complementary function: y = A + Be^-kx What would the suggested form of the particular solution be? "Cx" ?

Homework Statement U[SIZE="1"]xx +u(x,y)=0 Homework Equations ? The Attempt at a Solution Step 1) u(x,y)=A(x)B(y) Step 2) u[SIZE="1"]xx=d^u/dx^2 Step 3) d^u/dx^2 + A(x)B(y) = 0 Step 4) d^u/dx^2 = -[A(x)B(y)] (?) I have no idea what I'm doing, so small words would be useful.

In an investigation of a physics problem, I ran into the following equation: d^2(y)/(dt)^2 = k * y * (y^2 + c)^-1.5 I know how to solve separable first order differential equations but this one seems to be beyond me. Assistance?

Time dependent perturbation theory... second order term... For some reason they replace <E_{n}|H_{0}^2|E_{m}> with \Sigma<E_{n}|H_{0}|E_{i}><E_{i}|H_{0}|E_{m}> I know why they are allowed to do this, what I don't understand is how it makes my life better?

I am familiar with how to solve a second order, non-homogenous DE with constants, i.e. \frac {\partial^2X(t)}{\partial t^2} + \frac{\partial X(t)}{\partial t} = C by first solving the homogenous eqn, then setting the equation equal to a constant, yielding a sol'n of X(t)= Ae^{0}+...

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...

can any1 help me solve this? d2x/dt2 = -(k/m)*x -g at x= 0, t=0, v=sqrt(u^2-2gh) what is x?? can show the steps?

I need some help with power series. I can't remember how to find a power series center around a point. example question: y"-xy'-y=0, x=1 I don't how to start this.

Does anyone know how to solve this? \frac {d^2V(t)}{dt^2} + \frac{V(t)}{w} = \frac{Vm}{w}

Dear All, I have a Problem about a 2nd order ode. I don't know how it can be solved with Matlab. If someone know about it then please let me know. I need to get the values of x & y. All other values are known. The equation is: [ M + mf mf mf mf ][ ¨x ¨y...

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'm have a lot of trouble trying to find the general solution to the following D.E. y'' + 6.4y' + 10.24y = e^(-3.2x) I get the homogeneous solution as C1*e^(-3.2x)+C2*x*e^(-3.2x) and the particular solution as 0 So a general solution of Y=C1*e^(-3.2x)+C2*x*e^(-3.2x) I know my solution is...

Given:Second order ODE: x" + 2x' + 3x = 0 Find: a) Write equation as first order ODE b) Apply eigenvalue method to find general soln Solution: Part a, is easy a) y' = -2y - 3x now, how do I do part b? Do I solve it as a [1x2] matrix?

Solve the following for y(x); y'' - 3y' + 2y = 0 I kind of know what to do up to a point but after that I`m stuck (bad notes and no textbook!). Here`s what i`ve done so far, if someone could hint as how to finish this question i should be able to do the other 9 I have. let y =...

Hello everyone! My professor was going over a problem real fast for the exam and now that i went over it again, I'm lost on how he did this last step. He is using a method called Abels Theorum. THe problem says: Find a second solution of the given differential equation: t^2y''+3ty' + y = 0...

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! I had a question, I solved a problem very similar to this one but it has 2 real soltions which took the form of: y (x) = Ae^rx + Be^(rx) But now i have repeated roots: y(x) = e^(rx)*(A + Bx); HEre is the problem: Find y as a function of x if x^2 y'' - 11 x y' + 36 y =...

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!

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:

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...

I have come across the following question when revising for my upcoming exam, and wondered if anyone wouldn't mind giving me a hand and some hints as how to solve it. So far I have: F_{m} - k\frac{ds}{dt} = m\frac{d^2s}{dt^2} And now I'm stuck as to the solution of the equation, as its...

1st order, 2nd order Rate reactions HELP! I have read the section of my book over and over and studied the practice problems, but I still do not understand 1st order, 2nd order, or 0 order rate reactions. What does it mean to be of any particular order?

for the following question: y``+y`+9.25y=2+2x+x^2 my problem: yh=c1+c2e^(-x) suppose yp=c3x^2 + c4x+c5 then yp`=2c3x+c4 so yp``=2c3 then 2c3+2c3x+c4=2+2X+X^2 so c3=1, c4=1 so yp=x^2+x then y=c1+c2e^(-x)+x^2+x which implies c1=8 => y=8+c2e^(-x)+x^2+x so y`=-c2e^(-x)+2x+1...

Got this problem and we've been given a program which can solve for x, for the equation: Ax = b Where A = \left( \begin{array}{rrrrrr} b & c & 0 & 0 & \cdots & 0 \\ a & b & c & 0 & \cdots & 0\\ 0 & \ddots & \ddots & \ddots & & \vdots \\ \vdots & & \ddots & \ddots & \ddots & 0 \\ \vdots & & &...

Hi, can someone help me with the following question? I need to solve the ODE using series. y'' + 4y' + 3y = 0 Firstly, using the characteristic equation I know the general solution is of the form y\left( x \right) = Ae^{ - x} + Be^{ - 3x} . So I know roughly what I should get...

hi can anyone explain to me how to get the H value for runge kutta second method? I've searched everywhere online but i just don't understand it. if found h = tn - to/n?? i know what value of "to" is but no clue what values to put in for n and tn? thanks

for the following question: yy``=2y`^2 my problem: i don't have a clue how to get a hand on this one! any suggestions?

This problem is from section 5.2 in Boyce, DiPrima's Differential Equations 8th edition. (1 - x)\,y''\,+\,y\,=\,0 I get: 2\,a_2\,+\,a_0\,+\,\sum_{n\,=\,1}^{\infty}\,\left[(n\,+\,2)\,(n\,+\,1)\,a_{n\,+\,2}\,-\,n\,(n\,+\,1)\,a_{n\,+\,1}\,+\,a_n\right]\,x_n\,=\,0 Which leads to one...

This is problem number 1 (yes, one) in chapter 5.2 in Boyce, DiPrima, 8th edition. y'' - y = 0, x_0 = 0 Substituting the series for y and y-double prime: \sum_{n = 2}^{\infty} n (n - 1) a_n x^{n - 2} - \sum_{n = 0}^{\infty} a_n x^n = 0 Now, substituting n + 2 for n in first term...

The problem is this: Given sun of mass M and a body of mass m (M>>m) a distance r from the sun, find the time for the body to 'fall' into the sun (initially ignoring the radius of the sun). Our first equation is therefore \frac {d^2r}{dt^2} = \ddot{r} = \frac {GM}{r^2} . I am able to...