Differential equation Definition and 1000 Threads

Homework Statement Find an integrating factor for the first order linear differential equation \frac{dy}{dx} - \frac{y}{x} = xe^{2x} and hence find its general solution Homework Equations The Attempt at a Solution I found the integrating factor which is e^{-lnx} = x^{-1} and...

Mod note: HTML size = ... tags are not needed. You can make things look just fine using [ tex ] tags instead of [ itex ] tags. [/color] So, I was doing some stuff, messing around when I thought of something. What if I took a random physics formula and integrated it into the original function...

How to solve \( (x+1) y'' - (2x+5) y' + 2y = (x+1) e^x\) can we assume \(y_1 = (Ax+B) e^x \), then \(y_2= vy_1​\) Is this right? then solve for A and B Finally \( y = c_1 y_1 + c_2 y_2\)

Consider a circle of radius 'a' and centre (h,b) then the equation of the circle is given by (x-h)2 + (y-b)2 = a2 I expressed this in terms of differential equations which is - a= {[1+(dy/dx)2]3/2}/{d2y/dx2} According to my book - this equation indicates that 'a' is a...

Does it have an easy classification (elliptic, hyperbolic, parabolic, for example)? Or does the fact that it has an "i" in it make this impossible?

Hi I need to try and find the differential equation representing the attached circuit. My work is also being shown on the attachment. Can anyone confirm whether this is correct? If it is wrong could you please provide input as to why? Thanks. Sorry for the quality in advance.

I need explanations at the last part of this math solution. Question: Solve the differential equation: y' = (1 + 2/x)y Answer: ln|y| = x+ln(x^2)+c |y| = e^c.x^2.e^x y = Cx^2.e^x (C = +/-e^c is any constant that is not equals to 0) What I don't understand is this part where ...

Homework Statement 64y''+144y'=0 y1(0)=1 y'1(0)=0 and y2(0)=0 and y'2(0)=1 Homework Equations y1=c1*e^(r1*t) + c2*e^(r2*t)The Attempt at a Solution I start by finding the characteristic equation: 64r^2+144r=0 r1=-9/4 and r2=0 y1=c1e(r1*t) + c2e(r2*t) so I get y1=c1e^(-9/4 *t) + c2e^(0*t)...

THE PROBLEM : y(t) = e^(-t)*sin(t^2); with t0 = 0 and T = 3.14159. Find y_0, and use it to deduce the corresponding expression for f(t, y) (Your f should have both a t and a y in it. Simplify it to find the y!). This is for a MATLAB project. I've solved this differential equation (which we...

To Solve y’’ – 2 y’ – 3y = 64 e-x x ---------------(1) Using the method of undetermined coefficients : The roots of the homogeneous equation are 3 and -1, so the complimentary solution is y = c1 e3x + c2 e-x Then the guess for the particular solution of (1) is e-x x (Ax + B)...

Can anyone give some clues on how to solve this differential equation: f '(x) = 3 * f(x) Thanks!

Homework Statement \frac{dy}{dx}=\frac{2y - x + 7}{4x - 3y -18} Homework Equations The Attempt at a Solution I tried using v = y/x and got nothing. Same goes for trying to find an integrating factor to make the equation exact. I am given a hint, Find h and k so that the...

$(1-x^2)y'' - xy' + 4y =2 x \sqrt{1-x^2} $ Hint use the substitution $x =\sin t$ I used it and end with $\cos t y'' + \sin t y' - \frac{\sin t}{\cos t} y' + 4y = 2\sin t |\cos t| $ how to solve this i just want the name of the method

I'm given the differential dy/dx = x*y*sinx / (y+1) and I need to find its solution. I apply the following steps, (y+1)/y*dy = x*sinx*dx 1 + 1/y*dy = x*sinx*dx ∫ 1 + 1/y*dy = ∫ x*sinx*dx ...skipping a few steps for convenience I get the equation y + lny = -x*cosx + sinx My problem...

A particular solution to the differential equation y'' + 2y' + y = t^2 + 3? is t^2 - 4t +7 in the answers, but i get t^2 - 4t + 9 so where am i going wrong... y = Ay^2 + by + c y' = 2Ay + B y'' = 2A 2A + 2(2Ay + B) + Ay^2 +By + c = t^2 + 3 A(y^2) + (4A+B)y +(2A +2B+c) = t^2 + 0t + 3...

A first order DE models the rate of change, e.g. when decay is proportional to time we have the DE: dM/dt = -K.M; this is describing that rate of change mathematically. Am I correct in saying that a 2nd order DE describes the rate of rate of change? Also, can anyone explain any application of...

Homework Statement Find the explicit solution of dy/dx = 3y-3y2 Be sure to include any singular solutions in your answer Homework Equations Not sure... The Attempt at a Solution dy/dx = 3y-3y2 dy/(3y-3y2)=dx ∫(1/(3y-3y2))=(1/3)logy-(1/3)log(1-y) ∫(dx) = x + c x+c =...

Homework Statement This is the problem statement in the picture for exersize 14, it's rather long (pertaining to orthogonality - which I only understand what the definition of orthogonality is, which is the "(15)" on the side of the image below. http://postimage.org/image/oxhw2uf8p/...

Homework Statement A water tank is filled by an inflow x(t), the tank is emptied by the outflow y(t) The outflow if controlled by a resistance R The water depth in the tank is represented by d(t) The surface area of the water is A, independent of depth The tank is 1.5m high with a...

I saw this post at stackexchange: I ran across this post when trying to solve a homework problem. But I have no idea how he got that solution for that. When I use the Euler-Lagrange, I get this diff eq below. Here is the simplest form I have managed to get it in...

Homework Statement (3y4-11x2y2-28x4)dx-(4xy3)dy=0 Homework Equations My=Nx if equation is exact, if not, I can make it exact (I hope) by finding an integrating factor. The problem is I can't get the integrating factor to be a function of x or y only. The Attempt at a Solution Let stuff in...

Homework Statement A particle of mass m moves in the following (repulsive) field U(x) = α/x², α > 0, with α a constant parameter. Determine the (unique) trajectory of the particle, x(t), corresponding to the initial conditions of the form x(t0) = x0 > 0, x'(t0) =...

This is from section 2.3 in Griffith's book on the harmonic oscillator, and apparently this differential equation should be obvious (to move on in my reading, I need to understand this first). I'm not quite sure how to solve a second order ODE without constant coefficients, so help to get to the...

Homework Statement x\frac{dy}{dx} = 4yHomework Equations I'm not sure if there is a specific equation for these type of problems. My professor just says to separate the two different variables and then integrate them with respect to x.The Attempt at a Solution \frac{1}{4y} \frac{dy}{dx} =...

Homework Statement dy/dx +y=x Homework Equations none The Attempt at a Solution We know that x is the independent variable because y is differentiate with respect to it. And y is the dependent variable. Just wondering do you guys know why y is always a function of x in these...

Homework Statement A certain drug is being administered intravenously to a hospital patient. Fluid containing 5 mg/cm3 of the drug enters the patient’s bloodstream at a rate of 100 cm3/h. The drug is absorbed by body tissues or otherwise leaves the bloodstream at a rate proportional to the...

Folks, I am struggling to see what is happening here particularly when ## \displaystyle \sum_{i=1}^{n-1}## transforms into ##\displaystyle \int_{x_1^e}^{x_{n}^e}## ##\displaystyle 0=\sum_{i=1}^{n-1} \left [ \int_{x_i^e}^{x_{i+1}^e} (a \frac{dw}{dx} \frac{du}{dx}+cwu-wf )dx- \left [ w(x)...

I am trying to solve: (x + 1 + f(-x) )(1 - f ' (x) ) = x+1 f(0) = x_0 x in (-1,1) I approximated it numerically but any analytic method I try fails. Any ideas?

Homework Statement Solve the given differential equation by separation of variables. Homework Equations dP/dt = P - P2 The Attempt at a Solution This is no problem to "solve" except that Webassign (:cry:) wants to know the whole thing in terms of P. You end up with...

Homework Statement Suppose the clean water of a stream flows into Lake Alpha, then into Lake Beta, and then further downstream. The in and out flow for each lake is 200 liters per hour. Lake Alpha contains 500 thousand liters of water, and Lake Beta contains 400 thousand liters of water. A...

Homework Statement See attached photo Homework Equations The Attempt at a Solution I don't even know where to start on this problem. Usually, if I am given a possible solution to a DE, say y(t)=cos(t) as a solution to y''-y'+y=sin(t), I find whether it was a solution or not by manipulating it...

Homework Statement This is my first big differential equation that I have solved by myself, and I wanted to see if it is correct done, or what I have done wrong with it. Would really appreciate if somebody could take a look on it. y''+6y'+8y=0 when y(0)=1 and y'(0)=0 The Attempt at a Solution...

Homework Statement Is this differential equation linear or nonlinear? Assume that y' means dy/dx. Homework Equations 1. Homework Statement [/b] Is this differential equation linear or nonlinear? Assume that y' means dy/dx. Homework Equations \sqrt{xy'+2x2}=5 The Attempt...

Homework Statement Determine the values of r for which the given differential equation has solutions of the form y=t^r for t > 0.Homework Equations t^2 y'' - 13ty' + 48y = 0The Attempt at a Solution The program (online) has a thing that walks me through the question. It first had me find the...

Trouble with particular solution of differential equation - [SOLVED] Homework Statement Find the particular solution of the differential equation satisfying the initial condition The Attempt at a Solution I end up with (1/2)ln(-x^2+10x) which does satisfy the initial conditions...

In a lot of calculus texts, there's an example of an application of differential equations involving escape velocity. They write acceleration is dv/dt but then write it as \frac{dv}{ds}\frac{ds}{dt} That just looks like an application of the chain rule but what is the meaning of dv/ds...

Is there any general method to solve the following linear equation: [ D^6+a D^4+b D^2+(c-d sech^2(x))] y=0? Here, D=d/dx and a,b,c,d are constants.

hi the differential equation i am attempting to solve is: \frac {dP} {dx} = \frac {gP} {1+P/Psat} here is what I have done: \frac {dP} {dx} = \frac {gP*Psat} {Psat+P} divide both sides by \frac {Psat+P} {gP*Psat} to get: \frac {Psat+P} {P*Psat} \frac {dP} {dx} =g...

Hello, I tried to find the non linear second order differential solution of: diff(y(t), t, t)-(diff(y(t), t))+exp(y(t)) = 0 can anyone please help me? Kind regards, JJ

Hit a wall on this one...can anyone help with the next step? A(d2y/dt2)+B*(dy/dt)^2*(C*y^2+D*y+E)+F*y^-2=0 Thanks!

I have equations as C1*y1' = F*C2*y2 - C3*y1 y2' = C4 -B* C5*y3 - C6*y1 y2-C7=x(t)*y3 X(t) is a known function where F = 0 when y3<y1 1 when y3>y1 B=0 when C7<y3 1 when C7>y3 C's are constants so what I am thinking is at time t1 i will get the values for F...

I already posted this on a different website, so I'm just going to screenshot and post here.

Homework Statement Find a solution (Z2) of: z'' + 2z - 6(tanh(t))2z = 0 that is linearly independent of Z1 = sech2Homework Equations The Attempt at a Solution reduction of order gives you v''(t)(Z1(t))+v'(t)(2 * Z1'(t)) + v(t)(Z1''(t)+p(t)Z1'(t)) = 0 however the third term on the LHS can be...

Homework Statement Consider the equation x2y''-2xy'+2y=x with bountary conditions y(1)=0, y(2)=0. I don't know how to solve this without treating it as a Cauchy-Euler equation but I'm struggling because the equation equals x. The Attempt at a Solution By treating this as a...

Homework Statement Given the differential equation : \frac{dy}{dt} + a(t)*y = f(t) in which a and f are continuous functions in ℝ and verify: a(t) > c > 0 \forallt , lim f(t) = 0 Show that any solution of the differential equation...

Hi I am reading about the Langevin stochastic differential equation \frac{d}{dt}p = -\alpha p + f(t) where p is the momentum and f(t) the Langevin force. By definition <F(t)>=0 and <f(t)f(t')> = 2Dg(t-t'), where g is the second order correlation function. My question is, why is...

Homework Statement An object is falling from rest with air resistance modeled by $$kv_x$$. Where v_x is the object's velocity in the x-direction (downwards). Find an expression for the speed of the object as a function of time. Homework Equations $$mg-kv_x=m\frac{dv_x}{dt}$$ The...

Homework Statement y^(4)+y=0 Homework Equations Need to use de Moivre's formula to obtain answer. 3. The Attempt at a Solution . I can obtain the characteristic equation r^4=-1. From there I tried saying y_1 = cosx and y_2=sinx. However, my book has the answer listed as y=...

Homework Statement I took differential eq-n class more than a year ago and I am having problem solving this problem. 5(d^3y/dt^3)+3(d^2y/dt^2)+7(dy/dt)+y = 4(d^2f/dt^2), where f(t)=cos(t)-2sin(t) Homework Equations none The Attempt at a Solution First thing I did was to take the...

Can anyone help me on this equation. I want to find a solution for dr/dt. a, b and c are constants.