Differential equations Definition and 999 Threads

As a high school student, I enjoy studying mathematics on my spare time. Having recently worked through a textbook on vector calculus, I am in need of a textbook that will give me a solid introduction to differential equations. Any suggestions will help my search; however, I would prefer a...

Hi Fellows: If anyone has access to a copy of 'Differential Equations with Boundary-Value Problems (THIRD edition)' by Dennis G. Zill and Michael R. Cullen, I just need you to paste here or dictate to me on phone the following problem equations: 1. Problem no. 12 of chapter 4 review...

can anyone direct me to a website that gives adequate treatment of the numerical solution of partial differential equations, especially pertaining to problems which involve the use of the Crank-Nicolsen procedure?

Homework Statement Task is to write differential equation for this circuit. Homework Equations The Attempt at a Solution I'll try to solve the task, but now I want to know, is it possible to use voltage source instead of current source. For example, I can calculate ekvivalent...

Solve ##au_{x} + bu_{y} = f(x,y)##, where ##f(x,y)## is a given function. If ##a \neq 0##, write the solution in the form $$u(x,y) = (a^{2} + b^{2})^{\frac{-1}{2}} \int_{L} f ds + g(bx - ay)$$ (from Partial Differential Equations An Introduction, 2nd edition by Walter A. Strauss; pg. 10) I...

Homework Statement Solve d2y/dt2 = dx/dt2, if x = 0 and dx/dt = 1 when t = 0 Homework Equations The Attempt at a Solution d2y = dx I'm not exactly sure what to do here the fact that dt2 is under the denominator for both fractions is confusing memaybe its a typo? should it be d2y/dx2 = dx/dt?

Homework Statement Solve each of these differential equations by two different methods. \frac{dy}{dx} = 4(y+1)x^3Homework Equations Integrating factor \rho = \exp (\int(p(x) dx) Linear Equation \frac{dy}{dx} + p(x) y(x) = Q(x) The Attempt at a Solution So I first solved it using...

Homework Statement Model for learning in the form of a differential equation: \frac{dP}{dt}= k(M-P) Where P(t) measures the performance of someone learning a skill after training time (t), M is the maximum level of performance, and k is a positive constant. Solve this differential...

i got a book on differential equations that says a shortcut to solving the general differential equation f'(x)+p(x)f(x)=g(x) is to take the antiderivative of g(x) dx times exp(-p(x) dx times x) to solve for f(x) where dx represents the functions antiderivative. (i kno its supposed to represent...

I'm having trouble with this problem... I am almost certain that I have the first part correct which is solving the first order DiffEQ using an integrating factor. I think that I am computing the constant incorrectly. I have followed all steps, including the similar problem given on WileyPlus...

I can't seem to model this properly. This isn't an assignment, I'm just curious how this will go, lol. So I have this tank with an incoming feed stream with temperature Ti, and an output stream T. It has a jacket where q would be modified depending on the desired output stream T. So I...

Homework Statement Let's have a bucket flowing in water. Now we make a hole underwater. How fast will the bucket sink completely under water? It is a question from course called Ordinary Differential Equation, so I'm supposed to establish an ODE to solve this problem. I understand how to...

Homework Statement Task is to write differential equation for this circuit. E, R1, R2, R3, L are constants. Homework Equations Ul = L di/dt The Attempt at a Solution I guess, we have to use current method for each contour. 1st contour equation: E = U1 + U2 + Ul =...

Solve BVP by separating variables and using eigenfunction expansion method PDE:Ut-Uxx=e-2tsin(pi x/L) U=U(x,t),x(0,L) BC1:U(0,t)=0 BC2:U(L,t)=0 IC:U(x,0)=sin(pi x/L) U(x,t)=X(x)T(t),X''=(lambda) X ,lambda is the separation of parameter. I have calculated the basis functions...

I'm an engineering student, and in my next semester I want to take one of these 2 courses, differential equations or probability. I'm good in math but I'm taking some hard engineering courses and that's why I'm willing to choose the easiest of these 2 courses. Thank you for your advice.

Homework Statement $$y''-2y'+5y={ e }^{ x }cos2x$$ Homework Equations The Attempt at a Solution I still haven't completed the question but I just want to know if I'm on the right track. It's becoming ridiculously tiring to just complete 1 question. Is it supposed to be this long?

Since \frac{dy}{dx} is just considered notation, how can we treat it as an actual fraction when soliving differential equations? Could you, for instance, replace \frac{dy}{dx} with y'(x) in a differential equation and work it out?

A second order ode Py'' + Qy' + Ry = 0 is exact if there exists a first order ode Ay' + By such that (Ay' + By)' = Ay'' + (A' + B)y' + B'y = Py'' + Qy' + Ry = 0 How can one cast the analysis of this question in terms of exact differential equations? In other words, could somebody...

I am looking for help solving these two differential equations: 1. x'=-x 2. x'=x2, x(0)=x0 The solutions are x(t)=e-tx0, and x(t)=x0/(1-x0t). I just don't understand what steps were being done to get those solutions. If someone could point me in the right starting point or show me...

Here is the question: Here is a link to the question: http://answers.yahoo.com/question/index?qid=20130903134631AAuRmGn I have posted a link there to this topic so the OP can find my response.

How can i solve differential equations that are reducible to exact form? please explain each method. thanks

What math subject comes after partial differential equations for physics and electrical engineering majors?

I have read that, if you given a differential equation \frac{dy}{dx} = f(x,y), and can write it in the form \frac{dy}{dx} = h(x)g(y), then you can proceed with the following steps: \frac{dy}{g(y)} = h(x)dx integrating G(y) = H(x) + c Why are these steps vaild? I thought that one was not...

Question: Explain why you cannot solve the ordinary equation? x^2y'' + xy' + (x^2-1)y = 0 My attempt: I don't need to solve it, but just simply state why I can't with just differential equations So my answer is, This differential equation does have a solution, it's just not expressable in...

My weak spot in math is certainly DEs, I find them pretty boring, and fairly unattractive from an aesthetic point of view. I've spent some time with them while studying harmonic motion, and I've gotten OK at them when applied to this particular topic (aside from having trouble with solving...

I'm entering a differential equations course this coming semester. Is there anything I should review in the coming weeks?

Homework Statement x'= E - sin x + K sin (y-x) y'= E + sin y + K sin (x-y) E and K >0 Find fixed points for this system of equations Homework Equations This system is the form of coupled oscillators described in Strogatz. θ1'= ω1 + K sin (θ2-θ1) θ2'= ω2 + K sin (θ1-θ2)...

why are many fundamental laws of nature formulated in the form of differential equations?

How do I derive A? As you can see in the attachment, I tried to substitute x and expand the equation but I got stuck. How do I get rid of the δ and cos and sin to get the result in the end? Please help!

Homework Statement The problem is to solve: y''+ty'+e^{t}y=0, y(0)=0 and y'(0)=-1 Homework Equations The Attempt at a Solution My main issue is the following: I normally find the recursion relation, and then factor out the t^{whatever} and I know that the coefficient to this...

I have set myself the task of teaching my Freshman in high school brother Calculus, and today while reviewing some topics I saw something I didn't see before. To start out, I let y = ln[x] => x = e^y Obviously, we know that y' = 1/x = e^-y So, I "discovered" that one can define the...

I quote a question from Yahoo! Answers I have given a link to the topic there so the OP can see my response.

Can anyone tell me how the book arrived at the portion that I underlined in the paint document?

Homework Statement Given: y''[t] + 25 y[t] = 0 I know that the solution to this DE is of the form: y[t] = K1 E^(-5 i t) + K2 ​​E ^(5 i t) I get that, that makes sense to me, however when I look in old DE books I see the solution to the same problem written as: C1 Cos[5 t] + C2...

How do you make a differential equation for such? Say for example. I have two reactions in series, A → R and R → S going in a gas-phase reaction. If I'm correct, the ODE for the conversion of A is dXA/dt = kA*[(NAo/vo)*(1-XA)/(1+δA*YAo*XA)]*[(vo/NAo)*(1+δA*YAo*XA)]. I don't know now...

Homework Statement The problem states d^2y/dt^2 +15y= cost4t + 2sin t initial conditions y(0)=y'(0)=0 Homework Equations The Attempt at a Solution All I have is this r^2+15=0 making r(+-)=√15 and making yh= C1cos√15+C2√15 the next part includes solve for...

I have a problem which in involves a second order differential equations with imaginary roots and I can seem to know how to finish the problem. d^2y/dt^2 +15y =cos 4t+2 sin t this is what I got so far r^2+15=0 for the homogeneous part r=+-(√15) Yh=C1cos√15+C2sin√15 now is...

dy/dt = 2 - 2ty y(0) = 1 I am not asked to solve this (I know it's not easy to solve), but what I am asked is, "for large values of t is the solution y(t) greater than, less than, or equal to 1/t"? I would think less than because 1/e^(t^2) converges faster than 1/t, but at the same...

Homework Statement I have to find the differential of (y-xy')^2=x^2+y^2.Now,I have solved hom. equations but this is different because there are two y'. I know how to prove that it is a hom. equation of degree zero, so we can skip that, but how to solve this? Some hints would be highly...

I was asked to formulate the equations governing the rotation of a body moving without any external moments acting about its centre of mass in terms of a coupled system of first order, nonlinear differential equations. I decided to go with the Euler equations, and I ended up with this...

Homework Statement x' = \begin{pmatrix}0&1&3\\2&-1&2\\-1&0&-2\end{pmatrix}*x The Attempt at a Solution I've found the repeated eigenvalues to be λ_{1,2,3}=-1 I've also found the first (and only non zero eigenvector) to be \begin{pmatrix}1&2&-1\end{pmatrix}, but I'm not entirely...

Homework Statement \dfrac{\partial^2 \varphi }{ \partial x^2} - \dfrac{\partial ^2 \varphi }{\partial t^2} = 1 Initial Conditions: \varphi (x, 0) = 1; \varphi_t (x, 0) = 1 Boundary Condition: \varphi (0, t) = 1 On 0 \leq x < \infty, 0 \leq t < \infty...

Homework Statement I need to solve two differential equations to find a population function P(t). I am able to do this with problems like Newtons law of cooling: dT/dt=-k(T-Ta) solves to: dT=-k(T-Ta) dt ∫1/(T-Ta)dT=∫-k dt Ln(T-Ta)=-kt e-kt=T-Ta T=Ta+E-kt However I have been...

Homework Statement Hi, It's been a while since I have taken differential equations. How do I solve an equation like this: k_{1}\frac{d^{2}V_{x}(t)}{dt^{2}}+k_{2}\frac{dV_{x}(t)}{dt}+k_{3}V_{x}(t)=0 Homework Equations The Attempt at a Solution I have looked through my...

im in calculus 2 right now and we are doing differential equaitons right now. I am confused as to why when i find the integrating factor I(x)=e^(∫p(x) and when i multiply both sides i get e^∫(p(x))[(dy/dx)+p(x)*y]=d(e^(p(x)dx)*y) how are they equal. i will give an example. (dy/dx)+y=x*e^(x)...

Homework Statement Suppose the motion of a spring has natural frequency 1/2 and is undamped. If the weight attached is 32lb, write a differential equation describing the motion. Homework Equations my''+ky=F_ocosωt 32y"+8y=? ω_o= (k/m)^.5 The Attempt at a Solution → .5=(k/32)^.5 → k=8...

My textbook defines a solution to a differential equation to be a function f(x) such that when substituted into the equation gives a true statement. What I'm confused about are singular solutions. For example the logistic equation: dP/dt = rP(1-P/K) where r and K are constants. My textbook says...

Homework Statement I have a differential equation of the form \frac{dZ}{d\theta} + cZ = a cos \theta + b sin \theta Where Z = \frac{1}{2}\dot{\theta}^{2} I need to find the general solution of this equation. a, b and c are all constants. Homework Equations The questions suggests using...

y(x)=A*e^(λx) ; y'=λy attempt at solution: y'(x)= Ae^(λx)*λ λy= Ae^(λx)*λ divide by λ, which cancel. then i get: y=Ae^(λx) i want to say the differential equation holds but the issue i see is that y' and y'(x) are not equal derivatives, so my final answer is that the...

I need to find a,b,c,d, and e. I know how to do these problems the normal way but now he's giving us the answer and asking us to work backwards. I'm stumped. I think I night need to use some sord of system of equations but I'm not sure what it would look like..