Differential equations Definition and 999 Threads

At my school, Physics majors are the only ones who HAVE to take PDE, math majors and engineers have the option as an elective, but none of them do that because it has the reputation of being the most difficult math course at my school. I'm going into Calc III in the spring, then DE is next...

Homework Statement y'' + y' + y = 1 + x + x2 Homework Equations y = Ʃ CN*xN N starts at 0 y' = Ʃ N*CN*x(N-1) N starts at 1 y'' = Ʃ N*(N-1)*CN*x(N-2) N starts at 2 [b]3. The Attempt at a Solution [/] I know how solve the equations...

Homework Statement Solve the following differential equation: f"(x)=sinx x(0)=0, x'(0)=1 Homework Equations x(0)=0, x'(0)=1 The Attempt at a Solution f"(x)=sin(x) integrate, f'(x)=-cos(x)+C1 f'(0)=-cos(0)+C1=1 => C1=2 C1=2 f'(x)=-cos(x)+2 f(x)=-sin(x)+2x+C2...

The complete question I've been given: The Rossler equations are formally defined as dx/dt=−y−z dy/dt=x+ay dz/dt=b+z(x−c). Let us suppose that a=0.2, b=0.2, c=5.7, x(0)=y(0)=z(0)=0, t∈[0,400]. Let v1(t) be the solution to the given initial value problem, and let v2(t) be the solution of the...

Homework Statement A series RLC circuit has an electromotive force given by E=200e^(-100t) V, a resistor of 80 ohms, an inductor of 0.2 H, and capacitor of 5x10^-6 F. If the initial current and charge on the capacitor are zero, find the current at any time t>0. Homework Equations ...

Homework Statement solve: 160y''=160g-ky y(0)=-200 and y'(0)=0 2. The attempt at a solution I tried to use guess and check to solve this equation, but it didn't turn out nice at all... y''=9.8 - (ky)/160 y''+(ky)/160 = 9.8, guess y=e^(λt), y'=λe^(λt), y''=λ^2e^(λt) : this gives...

Hello Im new here, I hope I'm not disturbing anyone. Following this guide below, I am trying to find two 2. order differential equations, one for q1'' and one for q2'', describing the movement of the double pendulum. I have no problems with the mathematics, but when the guide tells me to...

We know that there are a few forms for 1st order differential equations. Second-order differential equations have an extra term with an x in it. My conjecture is that third-order differential equations have another extra term with an x^2 in it. A friend of mine agrees with this. Is this true and...

Homework Statement Find the indicial roots of the following Differential Equation: xy'' - y' + x3y = 0 Homework Equations y = Ʃ[n=0 to infinity]cnxn+r y' = Ʃ[n=0 to infinity](n+r)cnxn+r-1 y'' = Ʃ[n=0 to infinity](r+r)(n+r-1)cnxn+r-2 The Attempt at a Solution Plugging these values into the...

Dear all, I am interested in solving the following type of system of differential equations for η(x): (1) ∫η(x)ω(x)=0 (2) ∫η'(x)ω(x)=0 for known ω(x), and known limits of the integral. Does this type of equations have a name? Can someone help me to find some reference? Thanks a ton...

Homework Statement \frac{d^{2}y}{dx^{2}} = y\frac{dy}{dx} Homework Equations Let v = \frac{dy}{dx} and v\frac{dv}{dy} = \frac{d^{2}y}{dx^{2}} The Attempt at a Solution The question can be rewritten as: v\frac{dv}{dy} = yv \frac{dv}{dy} = y. (v =/=0 ) This is very easy...

Would anyone be able to go through some of the steps for these problems? 1. The birth rate in a state is 2% per year and the death rate is 1.3% per year. The current population of the state is 8,000,000. a) Write a differential equation which models the population of the state. Be sure to...

Hello, I was wondering if anyone could suggest a good book on "beginner's" differential equations. I am at an undergraduate level, it that helps you gage the content. thanks in advance

Hi! I'm working with my PhD thesis at the moment, and I've stumbled upon a pretty involved problem. What I have is a system of equations like this: \frac{dx}{dt} = A \cos(z) \frac{dy}{dt} = B x \frac{dx}{dt} \frac{dz}{dt} = y where A and B are constants. I also have a stochastic term to z...

*URGENT*Damped Harmonic Motion (Differential Equations) A damped harmonic oscillator satisfies the following equation: d2x/dt2 = − 5x − 2dx/dt (a) By assuming a trial function of the form x = A e^qt, determine the solution of this equation "from scratch." Express your final answer as a real...

Hi guys, I am a Erasmus student in Vienna. Due to the difference between the plans in my home universtity and Vienna, I have to deal with having to take Parcial differential equations without having done Differential Equations 1 or 2. In accordance with my university, I should take here...

Homework Statement Find the general solution to the following differential equations y'1 = -12y1 + 13y2 +10y3 y'2 = 4y1 - 3y2 - 4y3 y'3 = -21y1 +21y2 +19y3 The Attempt at a Solution I'm a little unsure about what to do at the end, or what form to put it in. The eigenvalues are λ1 =...

Homework Statement w= f(x,y) x = u + v Verify that Wxx - Wyy = Wuv y = u - v Homework Equations The Attempt at a Solution I know how to find Wu or Wv but I have no idea on how to proceed to find the 2nd order derivative (or 3rd,4rth etc.. obviously). I...

Homework Statement Here is the entire problem set, but (obviously) you don't have to do it all, if you could just give me a few hints on where to even start, because I am completely lost. Recall that we found the solutions of the Schrodinger equations (x^2 - \partial_x ^2) V_n(x) =...

Hi, I have to modelize the buckling of a column and I've come up with this system: N'(x) + N(x) \theta ' (x) \theta (x) - Q \theta ' (x) + f = 0 Q'(x) + N(x) \theta ' (x) + Q \theta ' (x) \theta (x) = 0 with f a constant The coefficients (thetas) are not constants. I've written it...

Hello all. I am having a very serious problem. The question states: Find the value(s) of δ such that the solution of the initial-value problem y'' − 4y = sin x; where y(0) = δ and y'(0) = 0 is bounded. I have no problem "solving"...

Can anyone help with these problems? I have no idea where to start. What is the general approach? Determine the solution of ∂ρ/∂t = (sin x)ρ which satisfies ρ(x,0) = cos x. Determine the solution of ∂ρ/∂t = ρ which satisfies ρ(x,t) = 1 + sin x along x =-2t. Relevant equations: ∂ρ/∂t +...

Linearize and classify the fixed points of \frac{d\theta1}{dt} = \Omega + sin \theta1 + \frac{1}{2} (sin\theta1 + sin\theta2) \frac{d\theta2}{dt} = \Omega + sin \theta2 + \frac{1}{2} (sin\theta1 + sin\theta2) I know that if the absolute value of omega is less than two, there will be 4...

Here's the problem i need help on. It can be found in Nagle's Differential Equations 8th edition chapter 8.3 number 32. http://hostingbytes.us/images/3/6025942.jpg i first tried to solve this using the power series and got: a2=a0 a(k+2) = 2ak/(k+2) after this, i have no idea how to...

About serval differential equations where A, B, D, g, \chi, c are functions of r \begin{eqnarray} &-\frac{{\chi}'}{r}+\frac{c'}{c}\left(\frac{g'}{g} -{\chi}'\right)=\frac{e^{\chi}(q A B)^2}{r^2 g^2 c^2}& \\ &c c''+c c'\left(\frac{g'}{g}+\frac{2}{r} -\frac{{\chi}'}{2} \right)=-\frac{B'^2}{2...

1. A body of mass 2kg is initially at rest and is acted upon by a force of (v - 4) Newtons where v is the velocity in m/s. The body moves in a straight line as a result of the force. 2. a. Show that the acceleration of the body is given by dv/dt = (v - 4) / 2 b. Solve the differential...

I'm currently studying ODE's from Boyce's 'Elementary differential equations and Boundary value problems', It's a good book and it also explains some physical applications of differential equations, but I'm looking for a book that its main topic is about how to write differential equations for...

Hi, Could some one help me to solve the equations ? dX =sqrt(X) dB where X is a process; B is a Brownian motion with B(0,w) =0;sqrt(X) is squart root of X.

Homework Statement Solve the following differential equation for q(t) (position): q''-qω^2 = C, where C is a time-independant value (basically a constant)The Attempt at a Solution This equation is not homogeneous, therefore it must be non-homogeneous. However, in every definition of...

I have following Differential Equations a1*x2+b2*x1-c*cos(int(x3))*x4=d -c*cos(int(x3))*x2-a2*sin(int(x3))+b2*x4=0 where a1,b2,c,d,a2,b2 are constants and x1=theta_dot; x2=theta_ddot; x3=alpha_dot; x4=alpha_ddot I want to solve these equations for x1,x2,x3,x4 and want to plot with time.

When it is stated that a certain formula is solution to a differential equation, what does that mean in the physical world. What is the significance of a certain formula being a solution to a differential equation?

Hello experts! Hope all of you will be fine. I have an equation i.e. xy=c And we all know it is hyperbola. Now I say "graph some of the hyperbolas xy=c". Then kindly tell me how can we extract more than 1 graph from this single equation? And you will write the differential equations for...

Homework Statement Solve the DE subject to y(1)=0. Forconvenience let k=v_r/v_s. First let me apologize for the way it is written but I don't know how to use software like other on other posts I see. Homework Equations (dy/dx)= (v_s*y - v_r*sqrt(x^2+y^2)) / (v_s*x) this may be...

Homework Statement Not exactly a problem, more an example that has me confused :s \frac{dN}{dt}=\kappa N-(\kappa/a^{2})N This describes a population model where N is the population, \kappa is the net births (ie: births less deaths) and it doesn't tell you what a is (this in all the...

Hi, I was reading a paper on control of the 1-D heat equation with boundary control, the equation being \frac{\partial u(x,t)}{\partial x}= \frac{\partial^2 u(x,t)}{\partial x^2} with boundary conditions: u(0,t)=0 and u_x(1,t)=w(t), where w(t) is the control input. The authors...

Homework Statement I've been having problems with a number of these things, here's the first one: y'' -2y' -3y = -3te-t Homework Equations I know that the general solution will be y = yh + yp where yh is the general solution to the homogeneous equation, and yp is the particular...

If u(x,y) and v(x,y) are two integrating factors of a diff eqn M(x,y)dx + N(x,y)dy, u/v is not a constant, then u(x,y) = cv(x,y) is a solution to the differential eqn, for every constant c.

Homework Statement One model for the spread of rumor is that the rate of spread is proportional to the product of the fraction y of the population who have heard the rumor and the fraction who have not heard the rumor. i) Write a differential equation that is satisfied by y ii) Solve the...

I'm given: 1. \frac{dX}{dt}=(X-1)(1-2X) 2. ln(\frac{2X-1}{X-1})=t and asked to verify that it is an implicit solution to the first order DE given. I successfully derived the second equation there to get: \frac{dX}{dt}=\frac{-1}{(2X-1)(X-1)} So now what? I tried several things and...

i have to solve the following differential equation : dy/ dx + y = f(x) where f (x) = 2, 0 <= x < 1 and 0 if x >=1 and y (0)=0. please explain how to solve it as it involves a discontinuous function ? I am stuck while computing after computing the integrating factor e^x. Please suggest how...

Hi! I think I have to ask this since I'm having health problems- from Kreyszig, for xy'=-y how do you verify the solution y=h(x)=clnx by differentiating y'=h'(x)=-clnx^2? I don't see how you get the x^2 term also for ODEs the solution is on an open interval a<x<b but how does it include...

Homework Statement Is the following equation a linear ODE? \frac{d^{2}R}{dt^{2}}=-\frac{k}{R^{2}} where k is a constant Homework Equations A linear ordinary differential equation can be written in the following form: a_{n}\left ( x \right )\frac{{d}^{n}y}{{d}x^{n}}+a_{n-1}\left ( x \right...

Homework Statement Consider the system X'(t)=AX+B(t) where: A = [0 0 -1] [1 0 -3] [0 1 -3] and B(t)= [e-3t] [et] [3 ] Find X(t) by frist determining P such that P-1AP=J is in Jordan form and then solving the three simple equations directly. Homework Equations...

Homework Statement Find a second order differential ewuation for which three functions y=2e^-t, y=2te^-t, y=e^(-t+1) are solutions. Homework Equations The Attempt at a Solution

Homework Statement 1. Find he solution of the initial value problem: x^2 (dy)/(dx) = 4y y(1)=2 2. Find the general solution of the differential equation: (dy)/(dx) - 2y = e^(5x) The Attempt at a Solution i'm completely confused by this, no idea where to start. If...

Consider a string of length 5 which is fixed at its ends at x = 0 and x = 5. The speed of waves along the string is v = 2 and the displacement of points on a string is defined by the function f(x,t). At the initial time the string is pulled into the shape of a triangle, defined by f(x,0) =...

I have to solve the differential equation (y')^2= 4y to verify the general solution curves and singular solution curves. Determine the points (a,b) in the plane for which the initial value problem (y')^2= 4y, y(a)= b has (a) no solution , (b) infinitely many solutions (that are defined for...

I have been given an equation : r^2 ( d^2R/dr^2) + 2r(dR/dr) - lambda*R = 0 It says to assume R~ r^β Then i can't seem to spot how from that information we can produce this equation: β(β − 1) rβ + 2β rβ − λ rβ = 0 Any help would be appreciated, thanks.

Homework Statement (b) Find the differential equation for which –4xy3 + 4xy3sin(x) = –1 is an implicit solution on the interval (0, pi/2). Write your answer in the form dy/dx = f (x,y) where f (x, y) depends on both x and y. The Attempt at a Solution I'm not too sure on how to go about...

Homework Statement Using power series, find solutions to the following DE y' + y= x^2, y(1)= 2 and xo=1 Homework Equations y(x)=an\sum(x-xo)^n for n=1 to infinity The Attempt at a Solution See the attachment NOTE: I only want to find a way to collect all the x...