Differential equation Definition and 1000 Threads

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...

Homework Statement Inside the earth, the force of gravity is proportional to the distance from the center. If a hole is drilled through the Earth from pole to pole and a rock is dropped in the hole, with what velocity will it reach the center? The Attempt at a Solution I think that the...

Homework Statement If d^2s/dt^2 = a, given that ds/dt = u and s = 0, when t = 0, where a, u are constants show that s = ut + .5at^2 2. The attempt at a solution du/dt = a cross multiplying and then integrating and we get u = at ds/dt = at cross multiply and...

I have to solve the differential equation y''+(1-t) y' + y= sin(2t) can someone judge this? How could I continue it? y=\sum_{n=0}^{∞}{a_{n} t^{n}} y'=\sum_{n=1}^{∞}{a_{n} n t^{n-1}} y''=\sum_{n=2}^{∞}{a_{n} n(n-1) t^{n-2}} sin(2t)=\sum_{n=0}^{∞}{\frac{2^{2n}}{2n!} t^{2n}} y''+(1-t) y'...

Friends I have one doubt Below given equation is linear or non linear :)

EDIT: my problem is solved, thank you to those who helped Homework Statement Solve: x y^{\prime \prime} = y^{\prime} \log (\frac{y^{\prime}}{x}) Note: This is the first part of an undergraduate applications course in differential equations. We were taught to solve second order...

Task 7 Show that y=(1/4)tsin2t satisfies equation d2y/dt2+4y=cos2t Find the general solution and deduce the solution which satisfies y(0)=0 and y'(0)=0. What happens as t increases? Solution In the end I stay with: y=Acos2t+Bsin2t+(1/4)tsin2t...

y"+2y'+y=2e^-t I tried to find the solution for this nonhomogenous diff. Equation but i could not. First i took a function Y(t)=Ae^-t but i was getting 0=2e^-t. To get rid of that i took another y'+y=2e^-t and found the solution y=2te^-t + ce^-t. Noticed that first part of this finding is...

Homework Statement Find the maximal ground reaction force for the limiting case where the speed at initial contact is equal 0 (Vo=0) expressing it as a mulitple of the body weight (mg) ω = √k/m Homework Equations Y1(t) = A sinωt + B cos ωt + g/ω^2 The Attempt at a Solution I...

Here is the DE: Δu(r,θ)=0, 1 ≤ r ≤ 2, 0 ≤ θ ≤ pi and here are the Boundary Conditions: u(1,θ)=sin(θ), u(2,θ)=0, u(r,0)=0, u(r,pi)=0 Based on the Boundary Conditions I believe this is half of an annulus. Using the 2D Laplace equation for polar coordinates, find the solution u(r,θ). I've...

Find the Fourier series solution to the differential equation x"+x=t It's given that x(0)=x(1)=0 So, I'm trying to find a Fourier serie to x(t) and f(t)=t, and I'm know it must a serie of sin... So here's my question...the limits of integration to the Bn, how do I define them? Will...

Homework Statement Hi, Just wondering if anyone knows how to solve the following as I am not sure where to start at all: y''' + 8y = xsin(2x) Any help would be great. Homework Equations The Attempt at a Solution I'm thinking solving the homogeneous DE y'''+8y = 0 and...

Homework Statement Consider the differential equation zZ'' + Z' + γ2 Z = 0, where Z = Z(z). Use the change of variables x = √(z/b) with b a constant to obtain the differential equation Z'' + (1/x)Z' + α2Z = 0, where Z = Z(x) and α= 2γ √b Homework Equations Maple commands The Attempt at a...

Homework Statement Given y_1=x is a solution, solve the differential equation Homework Equations y''+xy'-y=0 The Attempt at a Solution Since I am given y_1=x (is there a hotkey for adding TeX tags so I don't have to manually type these tags over and over? So tedious.) then I...

Homework Statement A bullet of mass m strikes an amor plate with initial velocity v0. As the bullet burrows into the plate, its motion is impeded by a frictional force which is directly proportional to the bullet's velocity. There are no other forces acting on the bullet. -Use Newton's Second...

What is the answer of this differential equation. ((d^2) r)/((ds)^2) +(m/(r^2)) -(nr/3)=0 the boundary conditions (i) r=a when s=0 and (ii) dr/ds =0 when r=b. m and n are constants.

Consider the first order differential equation dy/dy = f(t,y) = -16 t^3 y^2 with initial condition y(0)=1 Using second order Adams-Bashforth method, write a Fortran programming to generate an approximate solution to the problem. please forgive me for not trying because I really...

I have a problem that starts with the equation: r\frac{d^2u}{dr^2} + \frac{du}{dr} = 0 The solution I'm looking at says to do a substitution, letting u = r^m, which after differentiation and simplification results in: m^2 = 0 Up until this point, I understand (well, actually I don't...

Homework Statement Let ##y_1(x)= e^x## and ##y_2=x^2+1+e^x## solve the differential equation ##y^{'}+b(x)y=c(x)##. Find the overall solution of this differential equation. Homework Equations The Attempt at a Solution The overall solution => ##y=y_H+y_P## I don't know the english expression...

Mod note: Reinstated problem after poster deleted it. Homework Statement Just wondering if I did this correctly: ##y''+4y'+4y=e^{x}## and initial conditions ##y(0)=0; y'(0)=1## Homework Equations The Attempt at a Solution So I found the characteristic equation to be...

Homework Statement 1st problem - is this correctly done? \frac{dy}{dx} = (##x^2## - 1) ##y^2## , y(0) = 1 2nd problem - I really need help with this one. xy' - y = ##3x^2## , y(1) = 1 The Attempt at a Solution 1st problem: \frac{dy}{dx} = (##x^2## - 1) ##y^2## , y(0) = 1...

Homework Statement "Solve differential equation y''+y=2*cos x. Draw circuit of the equation and think about the strange behavior of the current." The attempt at a solution I was able to solve the equation, but I have no idea how to draw circuit about it, we haven't gone through this...

I have the following differential equation which I want to solve for y as a function of x \frac{dy}{dx}=\frac{C_{1}\left(C_{5}y+C_{6}\right)^{2}}{C_{2}\left(C_{3}y+C_{4}\right)-C_{7}\left(C_{5}y+C_{6}\right)^{6}} where C_{1},C_{2},C_{3},C_{4},C_{5},C_{6},C_{7} are constants. Can anyone...

Homework Statement A boy is on a boat, at a distance H from the shore, when he sees a girl (at the point on the shore where the distance is measured) running with a constant velocity u parallel to the shore. At that time, he moves towards her, with a speed v, in such a way, that the point of...

hello! I am facing some difficulties at the following exercise. "show that g(x)=x \cdot F(x) , where F(x)=\int_{0}^{x} {s(x)}dt , s(x)=\frac{sin(x)}{x} , satisfies the diffential equation xy'(x)-y(x)=xsin(x) , x ε R, and find all the solutions in this space. Show that the differential...

Homework Statement . Solve the differential equation: ##(3x^2-y^2)dy-2xydx=0##. The attempt at a solution. I thought this was an exact differential equation. If I call ##M(x,y)=-2xy## and ##N(x,y)=3x^2-y^2##, then the ODE is an exact differential equation if and only if ##\frac{\partial...

Hello - I asked a similar question before, but it was not resolved for me, and the person who answered was rude, so I did not continue the conversation. I read this here: http://tutorial.math.lamar.edu/Classes/DE/SecondOrderConcepts.aspx "If y_1(t) and y_2(t)are two solutions to a...

Homework Statement Solve x^{2}\times y'' - 4 \times x \times y' + 6 \times y = 0 for y(x) by first using the substitution v = ln(x) to obtain an equation involving y, dy/dv, d^2y/dv^2 and no x. Solve for y(v), then return to y(x). Homework Equations NA The Attempt at a Solution I know how...

Is there some systematic procedure to solve delay differential equation ? Here's one equation that I would like to solve \large \frac{1}{ \omega } \frac{dV_0(t)}{dt} = V_i(t) - \frac{V_o(t-T_d)}{k} where Td is the delay Thanks

Dear All, I have following first order nonlinear ordinary differential and i was wondering if you can suggest some method by which either i can get an exact solution or approaximate and converging perturbative solution. \frac{dx}{dt} = 2Wx + 2xy - 4x^{3}\frac{dy}{dt} = \gamma \, (x^{2} -...

Stochastic Differential Equation Hi there, I am trying to solve (analytically) a stochastic differential equation of the form: \frac{d^2}{dt^2}x +\left(k(t)+\delta k \ t\right)x)=0 Here \delta k is a random (gaussian) white noise. Note, that in the differential equation it is multiplied...

I have had this question on my mind for a long time When we solve a differential equation like this \frac{dT}{dx}=0 Do we do this ? \int\frac{dT}{dx}dx=\int0dx\int dT=\int0dxT =c_1 Because if we were to separate variables this doesn't work, we're just integrating both sides in respect...

Hi, i have to reduce the order of a 2nd order differential equation, to solve it with a numerical method. The equation is: \ddot{r}+a\dot{r}+\frac{b}{r^{2}}=0 with a,b\geq0 I tried to reduce it substituting \dot{r}=v, but i don't know what to do with the term \frac{b}{r^{2}} ...

I'm looking at this scenario where a car is moving and then shifts into neutral. Knowing the initial velocity, how can I derive a differential equation? I know the air drag and the frictional force... are there any other forces, like gravity, that should be included to make it realistic? I...

Hello everyone, I'm having trouble understanding the solutions to DE's of the form: ay''+by'+cy=f(t) We've gone over them in class, I've talked with my friends, and it just doesn't make any sense to me. I was wondering if anyone on here would help me understand the solutions, it would be...