Differential equation Definition and 1000 Threads

Homework Statement The question specifies the auxiliary equation given is (D^2 + D - 2) = (e^x)/(x) the method of variation of parameter must be used to find the particular solution to the right hand function. then finally the general soultion should be stated.Homework Equations variation of...

Homework Statement Without solving the differential equation, find the differential equation that solves Fourier transformation of given differential equation for ##a>0##. a) ##y^{'}+axy=0## b) For what ##a## is the solution of part a) an eigenfunction of Fourier Transform Homework Equations...

How do we solve a system of coupled differential equations written below? -\frac{d^2}{dr^2}\left( \begin{array}{c} \phi_{l,bg}(r) \\ \phi_{l,c}(r) \\ \end{array} \right)+ \left( \begin{array}{cc} f(r) & \alpha_1 \\ \alpha_2 & g(r)\\ \end{array} \right).\left( \begin{array}{c}...

is it possible to work backwards from a spectrum to which operator?

Homework Statement (x^2)y' = y Homework Equations The Attempt at a Solution Plugging in series everywhere I get the equation \sum na_{n}x^{n+1} = \sum a_{n}x^{n}. I try to set the coefficients for the corresponding powers equal, but when I do I don't get the correct answer. I also...

Homework Statement http://books.google.co.uk/books?id=93b3cjVJ2l4C&lpg=PA135&ots=8OtqgKwrQ2&dq=%22Two%20particles%20are%20connected%20by%20a%20spring%20of%20spring%20constant%20k%22%20and%20zero%20equilibrium%20%20length&pg=PA136#v=onepage&q&f=false Homework Equations All in the link...

Mod note: Thread moved from technical math section. The OP has already been notified that this is not a suitable start to a request for homework help.[/color] can anyone teach me how to start it? i really have no idea.. PART A

Hey, I'm not sure how to even approach this problem. It's not a simple ODE. Basically, I want to find the solution for Θ in terms of ε. The equation is \frac{1}{ε}*\frac{d}{dε}*(ε*\frac{dΘ}{dε})-β^{2}Θ=0 I tried to move the B^2 to the other side and I wasn't able to solve it that way. I...

The question ask to determine whether y = φ(x) = sqrt ( x - 1 ) is a solution of the differential equation 2yy' = 1.

Homework Statement Following a worked example in my book, I have been trying to get a solution for the equation \frac{d^2u}{dt^2} + \frac{k}{m}u = Fcos\omega t The book says that at resonance, i.e. when \omega_0 (the natural frequency) = \omega (the forcing frequency), the term F cos\omega...

Problem: Solve the differential equation: $$\left(\frac{1}{x}-\frac{y^2}{(x-y)^2}\right)\,dx+\left(\frac{x^2}{(x-y)^2}-\frac{1}{y}\right)\,dy=0$$ Attempt: Let $$M=\left(\frac{1}{x}-\frac{y^2}{(x-y)^2}\right)$$ and $$N=\left(\frac{x^2}{(x-y)^2}-\frac{1}{y}\right)$$ I noticed that...

Homework Statement Consider the RL circuit shown in the figure. Assume that the current ##i(t)## has reached a steady state with the switch at position ##A##. At time ##t = 0##, the switch is moved from position ##A## to position ##B##. http://imgur.com/dRIOrp0 If I use the image button...

Determine the differential equation relating \(v_i(t)\) and \(v_0(t)\) for the RLC circuit in the figure. Would this just be \[ v_i(t) = 3i + \frac{di}{dt} + 2\int i(t)dt \] but \(v_0 = 2\int i(t)dt\). Do I need write it as \(v_0\) or as \(2\int i(t)dt\)?

Homework Statement A pond forms as water collects in a conical depression of radius a and depth h. Suppose water flows in at a constant rate, k and is lost through evaporation at a rate proportional to the surface area. I was wondering whether anyone could give me some guidance on this...

Homework Statement I have been trying to solve this equation but keep coming to the same solution, which according to my book is not the correct one. Is anyone able to point out what I am doing wrong? \frac{dy}{dt}-\frac{1}{2}y=2cos(t) The Attempt at a Solution To solve, use...

Homework Statement How do I get d^2 y/dx^2 for a Cauchy-Euler, differential equation? Basically, how do I derive d^2 y/dx^2, as given in the following link (since I don't want to just memorize that equation)?: http://www.sosmath.com/diffeq/second/euler/euler.html Homework Equations *...

Find the general solution of the first order differential equation (y+x^{2}y)\frac{dy}{dx}=3x+xy^{2}, with y(1)=1. My attempt: \frac{y}{3+y^{2}}dy=\frac{x}{1+x^{2}}dx ∴ \frac{1}{2}\int \frac{2y}{3+y^{2}}dy=\frac{1}{2}\int \frac{2x}{1+x^2}dx...

Homework Statement a*dh(t)/dt + h(t) = b * sin(c*t) How can I get the equation for h(t) from this equation?? a,b,c are constant

I am looking for a general expression for an integrating factor μ(x,t) to solve the following diffential equation for x(t) \frac{dx}{dt} = \frac{x - f}{x} f = f(t) is an arbitrary function of t with f > 0 and df/dt < 0 Any ideas?

Homework Statement Find the general solution: 2xy \frac{dy}{dx} = y + x^4Homework Equations The Attempt at a Solution I have tried to solve this as a linear first order equation, a Bernoulli equation, and an exact equation. I'm not sure how to approach this, any ideas?

Homework Statement Find the general solution x(t) to the following differential equation: dx/dt = 2t/5xHomework Equations dx/dt = 2t/5x The Attempt at a Solution My solution is: ∫5xdx = ∫2tdt (5/2)x^2 = t^2 + C x^2 = (2/5)(t^2 + C) x = +-√[(2/5)(t^2 + C)] However, when I put the problem in...

A bacterial population B is known to have a rate of growth proportional to B itself. If between noon and 2pm the population triples, at what time no controls being exerted, should B becomes 100 times? what it was at noon? using this formula $\displaystyle P(t) \;=\;P_oe^{kt}$ please help me...

can you help me solve this, $\displaystyle (x^2+y^3+1)dx+x^4y^2dy=0$ I can't see any particular exact D.E form here. please help.

Homework Statement y^{\prime\prime}+y=\frac{1}{\sin x} Homework Equations The Attempt at a Solution I solved the homogenous equation: y=C_1\sin x+C_2\cos x, and then I tried to use method of variable the constant. But the equation system is rather hard. Do you know any other...

Homework Statement y=xy^\prime-\left(y^\prime\right)^2 Homework Equations The Attempt at a Solution Unfortunately, I do not have any good idea. I tried y=xt(x), but the equation only became worse.

please help me continue solving this, $\displaystyle \frac{dy}{dx}=\ln(x)-\ln(y)+\frac{x-y}{x+y}$ this is where I can get to, $\displaystyle \frac{dy}{dx}=\ln(\frac{x}{y})+\frac{x-y}{x+y}$ multiplying the 2nd term by $\frac{1}{x}$ $\displaystyle...

Homework Statement The equation: \frac{dx}{dt}=\frac{t^2+1}{x+2}. Where the initial value is: x(0) = -2. Homework Equations I believe you have to use the method of seperations of variables. The Attempt at a Solution So I multiplied both sides with x+2. Then I integrated...

find the desired equation. a.) $\displaystyle y=c_1+c_2e^{3x}$ taking two derivatives $\displaystyle \frac{dy}{dx}=3c_2e^{3x}$ $\displaystyle \frac{d^2y}{dx^2}=9c_2e^{3x}$ b.) $\displaystyle y=c_1e^{ax}\cos(bx)+c_2e^{ax}\sin(bx)$ a and b are parameters. can you help me continue with the...

just want to know what these symbols mean $\displaystyle M(x,y)\,dx+N(x,y)\,dy=0$ $\displaystyle \frac{dy}{dx}=f(x,y)$ $\displaystyle F(x,y,y'...y^n)=0$ what's M and N and the ordered pair (x,y) mean here. I don't understand my book. please explain.

Homework Statement Find the general solution: (y+1) dx + (4x - y) dy = 0 Homework Equations dy/dx + P(x)y = Q(x) (standard form) e^(∫ P(x) dx) (integrating factor) The Attempt at a Solution This exercise is in the chapter on linear equations, making non-exact equations exact. So I know I...

Homework Statement If α is an arbitrary constant and a a fixed constant show that xcos α + ysin α = a is the complete primitive of the equation (y - xdy/dx)^2 = a^2( 1 + (dy/dx)^2) Homework Equations The Attempt at a Solution FIrst I found the first derivative by...

So figuratively, I'm trying to win a nuclear war with a stick. :smile: I did not take any course in PDEs, I just self-studied some of them, and now I'm toast. :smile: First, please feel free to hurl rocks at me if my simplification is incorrect...

Find the differential equation or system of differential equations *** Find the differential equation or system of differential equations assoicated with the following flows a) ##\phi_t (x) = \frac{x}{\sqrt{1-2x^2t}} ## on ##{\mathbb R} ## b) ##\phi_t (x,y) = (xe^t, \frac{y}{1-y^t}) ## on...

Homework Statement Solve the inhomogenous partial differential equation \frac{∂^{2}u}{∂t^{2}}-\frac{∂^{2}u}{∂x^{2}}=-6u^{5}+(8+4ε)u^3-(2+4ε)u by using the NDSolve function in Mathematica for the interval [0,10] x [-5,5]. Homework Equations Initial conditions: u(0,x)= tanh(x)...

Problem: Solve: $$\frac{x\,dx-y\,dy}{x\,dy-y\,dx}=\sqrt{\frac{1+x^2-y^2}{x^2-y^2}}$$ Attempt: I rewrite the given differential equation as: $$\frac{(1/2)d(x^2-y^2)}{x^2d(y/x)}=\sqrt{\frac{1+x^2-y^2}{x^2-y^2}}$$ I thought of using the substitution $x^2-y^2=t^2$ but that doesn't seem to help...

Homework Statement Verify that the indicated expression is an implicit solution of the given first order differential equation. Find at least one explicit solution in each case. Give an interval I of definition of each solution. The differential equation is: \displaystyle \frac{dX}{dt} = (X...

Homework Statement Solve the initial value problem: y+(3x-xy+2)dy/dx = 0 , y(1)=1 I couldn't separate with y as a dependent variable, so I made x the dependent variable and I get this: dx/dy= x(1-2/y)-(2/y), in linear standard form: dx/dy+(3/y - 1)x = -2/y. Homework Equations...

In each of the following cases, we define a function : ##\phi##: ##{\mathbb R} \times {\mathbb R}^3 \rightarrow {\mathbb R}^3 ## . Determine in each case whether this function could be the flow of a differential equation, and write down the differential equation. (a) ##\phi_t(\vec{x}) =...

Homework Statement Hello, I was given an extension problem in a Dynamics lecture today and am struggling to solve it. It is a simple scenario: a particle of mass m is accelerating due to Galilean gravity, but is subject to a resistive force that is non-linear in the velocity of the particle...

Homework Statement A 400-gallon tank initially contains 200 gallons of water containing 2 parts per billion by weight of dioxin, an extremely potent carcinogen. Suppose water containing 5 parts per billion flows into the top of the tank at a rate of 4 gallons per minute. The water in the tank...

Homework Statement Given \frac{dx}{dt} + ax = Asin(ωt), x(0) = b Solve for x(t) Homework Equations The Attempt at a Solution I take the Laplace transform of both sides and get sX(s) - x(0) + aX(s) = \frac{Aω}{s^{2} + ω^{2}} X(s) = \frac{b}{s + a} + \frac{Aω}{(s^{2} + ω^{2})(s+1)} The...

I'm solving a differential equation to do with quadratic resistance and it seems to be acting very strangely - I get the opposite sign of answer than I should. If anybody could have a quick look through that would be much appreciated. For a particle moving downward and taking positive upwards...

can this equation y, = ycot(x) + sin(x) be reduced to a homogenous linear format? If yes, how? I tried the usual y=xv and the x=X+h, y=Y+k but doesn't seem to be working. Any ideas? Thanks just realized its in the form of dx/dy+Px=Q so I solved it by multiplying on B.S. by e∫Pdx and the...

Homework Statement https://www.physicsforums.com/attachment.php?attachmentid=65556&stc=1&d=1389570667 For those who can not see the screen shot here is the question... Suppose the population P of rodents satisfies the diff eq dP/dt = kP^2. Initially there are P(0) = 2 rodents, and their number...

2. Water drains out of an inverted conical tank at a rate proportional to the depth y of water in the tank. Write a differential equation for y as a function of time. My answer was dy/dt = ky. This was from a weekly homework set where there were only 5 problems. I feel like I am missing...

Differential Equation ---> Behaviour near these singular points Homework Statement Problem & Questions: (a) Determine the two singular points x_1 < x_2 of the differential equation (x^2 – 4) y'' + (2 – x) y' + (x^2 + 4x + 4) y = 0 (b) Which of the following statements correctly describes...

Kindly solve it and i need help to understand NON LINEAR Questions

I am trying to solve a homogeneous, first-order, linear, ordinary differential equation but am running into what I am sure is the wrong answer. However I can't identify what is wrong with my working?! $$\frac{dy}{dx}=\frac{-x+y}{x+y}=\frac{1-\frac{x}{y}}{1+\frac{x}{y}}.$$ Let $z=x/y$, so that...

dy/dx=2x+y^2 By the way, methods of solving linear differential equation are useless, such as integrating factor and Bernoulli method.

$$ xy'' - y' = 3x^{2} $$ $$ y' = p $$ $$ y'' = p' $$ $$ xp' - p =3x^{2} $$ $$ p' - \frac{1}{x}p = 3x $$ after multiplying by the integrating factor we get.. $$ \frac{1}{x}p' - \frac{1}{x^{2}}p =3 $$ so $$ [\frac{1}{x}p]' = 3? $$ I know that these two below are equal, but can someone please show...