Differential equation Definition and 1000 Threads

Homework Statement Find a solution of $$\frac{1}{x^2}\frac{\partial u(x,y)}{\partial x}+\frac{1}{y^3}\frac{\partial u(x,y)}{\partial y}=0$$ Which satisfies the condition ##\frac{\partial u(x,y)}{\partial x}\big |_{y=0}=x^3## for all ##x##. The Attempt at a Solution I get the following...

Homework Statement 2. Consider an electric circuit consisting of an inductor with inductance L Henrys, a resistor with resistance R Ohms and a capacitor with capacitance C Farads, connected in series with a voltage source of V Volts. The charge q(t) Coulombs on the capacitor at time t ≥ 0...

Homework Statement Solve (x-1)y''-xy'+y=0 , given x>1 and y1=ex Homework EquationsThe Attempt at a Solution I've tried solving it by multiplying everythin for (1/x-1), so my equation looks like: y''-(x/x-1)y'+y=0 (because x-1 is unequal to 0) (1) so now the equation has the...

Homework Statement Homework EquationsThe Attempt at a Solution integral[du]= Integral[xt ds] xt=18s2+3sT so, u=Integral[18s2+3sT] u=6s3+(3/2)s2T+C C=eT2 This is what I did and the solution is below. I'm unsure where the missing power on the (3/2)sT went in the u(s,t) equation.[/B]

Homework Statement Solve y''+(cosx)y=0 with power series (centered at 0) Homework Equations y(x) = Σ anxn The Attempt at a Solution I would just like for someone to check my work: I first computed (cosx)y like this: (cosx)y = (1-x2/2!+x4/4!+ ...)*(a0+a1x+a2x2 +...)...

Homework Statement I'm having difficulty deriving the differential equation, this is what I have so far. In order to solve it, I will be using Matlab, and I'll be using the equation dy/dx ≈ (y(x + dx) - y(x))/dx. Is my derivation correct so far? Homework Equations In picture. The Attempt at a...

Homework Statement Given a function g(t)=acosωt + bsinωt, where a and b are constants, show that g(t) is the real part of the complex function: keiΦeiωt for some k and Φ Remark: the complex expression keiΦ is called a phasor. If we know that g(t) has the form kcos(ωt+Φ) then we need know only...

Homework Statement Block 1 (mass 2 kg) is moving rightward at 10 m/s and block 2 (mass 5kg kg) is moving rightward at 3 m/s. The surface is frictionless, and a spring with spring constant of 1120 N/m is fixed on the left side on block 2. When the blocks collide, the compression of the spring is...

Homework Statement Find constants a and b such that y=ax + b is a solution to the differential equation dy/dx = 4x - 2y Homework EquationsThe Attempt at a Solution I already have the solution that is: a=4x-2 (ax+b) (I'm fine with this part) a = (4-2a) x - 2b (what happened here?) 4-2a=0...

Hello. I'm solving the second order nonlinear ODE, and I'm not sure that it's possible or not. Please help. A_0, B_0, C_0, a, b, c, e, p is all known constant. dA/dt = -(a+b*C)*B dB/dt = -p*c*A dC/dt = -(1-p)*e*A then I want to get a solution like A(t) = function of (A_0, B_0, C_0, a, b, c...

Homework Statement Solution of the differential equation ##(\cos x )dy = y (\sin x - y) dx , 0 < x < \dfrac{\pi}{2} ## is Homework EquationsThe Attempt at a Solution Only separation of variables, homogenous and linear DEs are in the syllabus, therefore it must be one of those. It obviously...

Homework Statement Trying to use change of variables to simplify the schrodinger equation. I'm clearly going wrong somewhere, but can't see where. Homework Equations [/B] Radial Schrodinger: -((hbar)2)/2M * [(1/r)(rψ)'' - l(l+1)/(r^2) ψ] - α(hbar)c/r ψ = Eψ The Attempt at a SolutionWe're...

The equations I'm getting when I solve the differential equations seem to imply that the amplitude of oscillation does not vary in time. For example, if I have x'' + ω02x = cos(ωt) If we suppose that ω≠ω0, then the general solution should look something like: x(t) = c1cos(ω0t) + c2sin(ω0t)...

The equations I'm getting when I solve the differential equations seem to imply that the amplitude of oscillation does not vary in time. For example, if I have x'' + ω02x = cos(ωt) If we suppose that ω≠ω0, then the general solution should look something like: x(t) = c1cos(ω0t) + c2sin(ω0t)...

I obtained an extra factor of ##\frac{1}{l^2}## in the first term on the LHS of (3.34). From (3.33), LHS ##=u^2\frac{d}{d\theta}(\frac{u^2}{m}\frac{du}{d\theta}\frac{dr}{du})-\frac{l^2u^3}{m}## ##=u^2\frac{d}{d\theta}(-\frac{1}{m}\frac{du}{d\theta})-\frac{l^2u^3}{m}##...

Homework Statement I am trying to find an equation for a free hanging chain of mass m and length L. The chain is hanging vertically downwards where x is measured vertically upwards from the free end of the chain and y is measured horizontally. Homework Equations [/B] I derived this...

Homework Statement dy/dx = (x-y+2) / (x+y-2) , by using x=X and y=Y+2 , form a differential equation . Homework EquationsThe Attempt at a Solution the author gave the answer as (Y^2) +(2XY) -(X^2)+A= 0 , while my answer is (Y^2) +(2XY) -(X^2)+A(X^4)= 0 is there anything wrong with my answer?

y" - 2xy' + my = 0 this is well known hermite diff eqn. now can anyone tell me what kind of conts is m?? what is the suitable value of m??

Hi I'm just having trouble wrapping my head around differential equations with matrices and vectors... For example: let y be a vector. let A(t) be an nxn matrix. I have the differential equation: dy/dt = A(t)y So I think I understand why the solution is y = ceA(t) But I'm having trouble...

I need to solve the well known momentum equation in 3D cylindrical coordinates: ρ(∂v/∂t +(v.∇)v)=A where A and the velocity v are both local vector variables. I am actually looking for the stationary solution to the equation, i.e. no ∂/∂t term) I have tried evolving the velocity and tried...

1. Homework Statement A tree is planted as a seedling of negligible height. The rate of increase of its height , in metres per year is given by ##0.2√(25-h)## a. explain why tree can't exceed 25 metres. answer⇒ ##dh/dt=0## when h=25 b. express t as a function of h answer⇒...

Homework Statement I am supposed to write a script that can solve the Schrödinger equation on a nonuniform grid. Homework Equations Finite element approximation to the second derivative as in: https://www.physicsforums.com/threads/nonuniform-finite-element-method.857334/#post-5382329 The...

Homework Statement Find the general solution to differential equation y''-6y'+9y=e^x((2x+1)\cos x+(x+3)\sin x) Homework Equations -Non homogeneous differential equation -Homogeneous differential equation with constant coefficients -Method of undetermined coefficients The Attempt at a Solution...

Homework Statement my ans is lnx = (-1/y) + c (-1/y) = lnx -c y = -1/ (lnx -c ) , but the answer given is (-1/ln x )+ C , how to get the answer given ? Homework EquationsThe Attempt at a Solution

Homework Statement Find the solution to: $$\frac{d^2}{dt^2} x + \omega^2 x = \delta (t)$$ Given the initial condition that ##x=0## for ##t<0##. First find the general solution to ##t>0## and ##t<0##. Homework Equations The Attempt at a Solution This looks like a non-homogeneous second...

Homework Statement The speed of a falling body might be based on the observation that the velocity of a falling object seems to increase the further it has fallen. Model the hypothesis "The speed of a falling object is proportional to the distance it has fallen" as a differential equation...

Are there any known analytical method to solve the equation $$ A\frac{d^2f(x)}{dx^2}+B\frac{df(x)}{dx}+Ce^{igx}f(x) = 0\hspace{1cm}? $$ All quantities appearing in that equation are complex except for ##g## and ##x##.

I tried to solve this differential equation: 2y+(y')^2+ax^b=0 ...but don't know what to do with it. Don't know what variable substitution to use. Tried Taylor series, but I get horrible nonlinear equations for the coefficients. Tried Mathematica, but it doesn't answer anything: In[20]:=...

Homework Statement [/B] This circuit solves some differential equation, the question is asking for the equation based on the circuit diagram imgur link: http://i.imgur.com/b1npQSK.pngHomework EquationsThe Attempt at a Solution I refer to the input terminal for -f(t)...the signal from it...

Homework Statement hello, I was reading through the textbook and I have a hard time to understand this part: Homework EquationsThe Attempt at a Solution haven't been dealing with derivatives for a while, i don't understand how it got ln |u(t)| from the first equation. Am I treating the...

Homework Statement I'm asked to use the transformation of v= 2x-y to solve dy/dx = (2x-y+4)/ (4x-2y +1) the answer given is (2/9)(6x-3y-2) +(7/9)ln(6x-3y-2) = x +c , i got (2/9)(6x-3y) +(7/9)ln(6x-3y-2) = x +c , what's wrong with my working ? Homework EquationsThe Attempt at a Solution

Homework Statement Solve the differential equation. -x2(dy/dx) + xy = x2y2 * sin(x) Homework Equations None. The Attempt at a Solution I first figured out that this was a Bernoulli's equation. I distributed the x2 to make it simpler. From there I divided everything by y2 to get y-2(dy/dx) +...

Homework Statement dy/dx = (x +y) / (x-y) , i am asked to find the first order differential equation , but the ans i gt is different from the ans given Homework EquationsThe Attempt at a Solution

Homework Statement i was given dy/dx = -(4x+4y) / (4x+4y-2) , v= x +y . I have tried to do ( as in the photo) , but I didn't get the ans , in the last line of my working , the V and x are not separable , which part of my working is wrong ? Homework EquationsThe Attempt at a Solution

I understand what is in the picture http://postimg.org/image/u5ib33kzb/ but the book goes on to say that the solution is thus of the form ## X_n = a_n sin \frac{n \pi x}{l} ## How does putting ##β=σ^2=\frac{n^2π^2}{l^2}## into (6.37) result in that?

My current understanding of differential equations is extremely shaky, and my vocabulary is probably very incorrect, but I'm curious about something I've recently seen in some Khan Academy videos (specifically this one) and in other situations with differential equations. It seems that the...

hey, need an idea for a paper on differential equations, which can be implemented in two or three days work. also it will be nice if that paper has graphs on it. any help would be most welcome thx

Homework Statement Question: Solve this differential equation dy/dt=1+y2 and y(π/4)=-1 Homework Equations The Attempt at a Solution dy/dt=1+y2 and y(π/4)=-1 dy/dt=1+y2 dy=(1+y2)dt dy/(1+y2)=dt ∫dy(1+y2)=∫dt tan-1(y)=t+c y(t)=tan(t)+c y(π/4)=tan(π/4)+c -1=1+c -2=c answer: y(t)=tan(t)-2

Hey guys, so my professor told me to take a look at an equation, because he thinks that there is a mistake. We are basically talking about exercise 6.3 (on last image). The pictures will show you the text, so that you have all the information, that I have http://puu.sh/mrNDl/ec19cdff63.png...

Homework Statement I am trying to obtain the hermite polynomial from the schrødinger equation for a har monic oscillator. My attempt is shown below. Thank you! The derivation is based on this site: http://www.physicspages.com/2011/02/08/harmonic-oscillator-series-solution/ The Attempt at a...

Hello. I forgot the reason why 2nd order differential equation has two independent solutions. (Here, source term is zero) Why 3 or 4 independent solutions are not possible? Please give me clear answer.

Homework Statement Homework Equations 3. The Attempt at a Solution [/B] Hello guys,I posted images since its easier to write equations.Please can someone help me check this, if this is correct so far, then i should be able to find the velocity at C, using kinetic energy?

Homework Statement A vat with 2000L of beer contains 4% alcohol (by volume). Beer with 6% alcohol is pumped into the vat at a rate of 20L/min and the mixture is pumped out at the same rate. What is the percentage of alcohol after an hour? Homework EquationsThe Attempt at a Solution At ##t =...

Homework Statement Find the general solution f(t) of the differential equation: f''(t) − f'(t) − 12f(t) = 36π . How many free parameters enter the solution, and why? Homework Equations f = fH + fP where fH is the homogeneous solution and fP is the particular solution. The Attempt at a...

Hello guys, I found this forum using google because I need help with simulating bungee jump model. I've already done that with zero initial values and it looks good but I want it more realistic : Let's say L is the length of rope so elasticity force starts acting when y=L so logically time...

Homework Statement Solve the differential equation: dy/dx = 2/(x+e^y) Homework EquationsThe Attempt at a Solution I tried to use the substitution v=x+e^y, but I didn't get very far: v’=1+e^y y’ v’-1=(v-x)y' y’ = (v’-1)/(v-x) (v’-1)/(v-x) (x+v-x)=2 V (v’-1)/(v-x)=2 vv’-v=2(v-x) vv’-3v=-2x...

Basically, I am confused by one question in a practice paper in which the equation is given as follows: dy/dx = e^-2y and I know the general solution is equal to : y = -0.5e^-2y + C which would make sense if it was direct integration however it seems to me it is in fact separable...

Can you advice the changes in this diff equation: $\d{y}{x}=\dfrac{y}{x^2+y^2}$

Homework Statement I need to solve the follwing differential equation $$(\frac{df}{dt}) \dfrac{4 n e^{4nf(t)}-9n e^{2nf(t)} (\frac{df}{dt})^2 + e^{2nf(t)} r^2 \frac{d^2f}{dt^2}+5n (\frac{df}{dt})^4 r^4 - r^4 \frac{d^2f}{dt^2} (\frac{df}{dt})^2}{-e^{2nf(t)}+ (\frac{df}{dt})^2 r^2}=0 $$...

Homework Statement ##\displaystyle (x+3)\frac{dy}{dx} = y - 2##, where x is not 3 and y is not 2. Homework EquationsThe Attempt at a Solution ##\displaystyle (x+3)\frac{dy}{dx} = y - 2## ##\displaystyle \frac{dy}{y-2} = \frac{dx}{x+3}## ##\displaystyle \int \frac{dy}{y-2} = \int...