Differential equations Definition and 999 Threads

solve the following differential equation with the suggested change of variables.

Specifically:

Homework Statement I am given (y^2 + y sin x cos y) dx + (xy + y cos x sin y) dy = 0, y(0) = π/2 . I need to solve this Homework EquationsThe Attempt at a Solution At this point they still aren't exact, so I gave up. I can't figure out what the problem is. Is it possible that I have to...

Hello everyone. So I wanted to get some opinions on what some of you thought was a better choice, as far taking PDE's or classical mechanics 2 goes. First let me start off by giving a little info; I've already taken calc 1-3 and ordinary differential equations, physics 1 & 2...

Hi folks, When you have a differential equation and the unknown function is complex, like in the Schrodinger equation, What methods should you use to solve it? I mean, there is a theory of complex functions, Laurent series, Cauchy integrals and so on, I guess if it would be possible to...

(1) ##\frac{d^{2}y}{dx^{2}}=0## (2) ##\frac{d^{2}y}{dx^{2}}=k^{2}y##, where k is a real positive number.

Homework Statement Find the full response. Assume Vin is a squarewave with Vpp =10V and Vamp = +5V Homework Equations KCL The Attempt at a Solution My teacher gave this solution but I don't really understand some parts of it. Full response = Natural response + forced response Thevenin...

Homework Statement Homework EquationsThe Attempt at a Solution Nodal Equations By property of OpAmp, V2=Vo eq1:\frac{V_{1}-V_{in}}{R_1}+\frac{V_{1}-V_{o}}{R_2}+C_2*(\dot{V_1}-\dot{Vo}) eq2: V_1=C_1R_2\dot{V_o}+V_o eq3: \dot{V_1}=C_1R_2\ddot{V_o}+\dot{V_o} Sub 2 & 3 into 1...

Homework Statement Identify the type of singularity at x=0 for these differential equations x*Sin[1/x]*y''[x]+y[x]==0 x^2*y''[x]+Sin[1/x]*y[x]==0 Homework Equations A Singular point is regular if f(x)(x-x_0)^n is defined as x approaches x_0 and is analytic in a near a neighborhood of that...

Are there differential equations that, for some reason, don't have a Green function? Are there conditions for a DE to satisfy so that it can have a Green function? Thanks

A one-dimensional dynamical system is given by $x′ = f(x), t \in [0,+\infty)$, where $f : \mathbb{R} \to \mathbb{R}$ is the smooth function defined as follows: $$f(x) = \begin{cases} x^4 \sin \left(\frac{1}{x}\right) & x \neq 0\\ 0 & x = 0. \end{cases}.$$ Find all the equilibrium points and...

Homework Statement Let ##A## and ##B## be square matrices, such that ##AB = \alpha BA##. Investigate, with which value of ##\alpha \in \mathbb{R}## the subspace ##N(B)## is ##A##-invariant. Homework Equations If ##S## is a subspace and ##A \in \mathbb{C}^{n \times n}##, we define multiplying...

<<Moderator's note: this is a spin-off of https://www.physicsforums.com/threads/how-long-to-learn-physics.891250/>> To Zapper. Some differential equations have no analytical solutions but some do. I remember a case where a co worker was using a computer to find the solution to x dot = 1 /...

Homework Statement Find the general solution to the differential equation: Homework Equations Separation of variables for solving 1st order separable differential equation. The Attempt at a Solution Using separation of variables, I can write: My questions are: 1) Am I correct to...

Hello, I have been working on a little movement system in a program called Game Maker: studio. The code works fine on the programming perspective, but something I did not expect happened: When I ran the code by adding to the speed while pressing a key, and every step passively subtracting from...

Homework Statement I'm not sure how to approach this. The question involves linear operators and a non-homogenous differential equation. Here is the question: https://s15.postimg.org/cdmw80157/Capture.png Homework Equations They are given in the question The Attempt at a Solution I really...

Homework Statement In this problem you will do numerical computer calculations. A skydiver of mass 75.0 kg jumps out of a plane at an altitude of 30.0 km above the surface of the Earth. His parachute fails to open. Assume there is no horizontal motion and the initial velocity is zero. We...

Homework Statement I Have a differential equation y'' -xy'-y=0 and I must solve it by means of a power series and find the general term. I actually solved the most of it but I have problem to decide it in term of a ∑ notation! Homework Equations y'' -xy'-y=0 The Attempt at a Solution I know...

Hello,I have a department elective course called "Differential equations theory" but I have no idea if it is going to be useful for me as a physicist (I'm interested in the theory/ minor math). The description of the course is as follows : The fundamental theorem of existence and autism, linear...

Homework Statement Find a solution \bf{\phi} of the system $$y'_1(t)=y_1(t)+y_2(t)+f(t)$$ $$y'_2(t)=y_1(t)+y_2(t)$$ where f(t) is a continuous function $$\bf{\phi} (0)=(0,0)$$ Homework Equations A hint was given to define ##v(t)=y_1(t)+y_2(t)## The Attempt at a Solution Using the suggested...

Homework Statement Find the general solution for the DE: t2y''-2y=0 Homework Equations These were given for other parts of the problem so I'm not sure if they're relevant. y1(t)=t2, y2(t)=t-1, y(1)=-2, y'(1)=-7 The Attempt at a Solution The t2 at the front was really stumping me and I'm not...

Hello, I was just wondering if there is a geometric interpretation of the trace in the same way that the determinant is the volume of the vectors that make up a parallelepiped. Thanks!

Homework Statement [/B] Its been a pretty long time since I've taken differential equations and I'm expected to know the solutions to the kinds of DEs below for my fluid mechanics class. In class my professor worked a 2nd order DE: dy2/dx2 = -k2*y and told us the way to think about it was to...

Hey guys :) So I'm looking to form equations that I can apply a Laplace transformation to. The mechanism specifically is a trailer jack - it converts rotational motion to linear motion. And its high torque provides a mechanical advantage to lifting heaving loads. Can anyone help me form...

I have the following linear differential equations: ##A\dot{x} + By = 0## ##C\dot{y} + Dx = 0## Where x and y are functions of t, and A through D are constants. I can solve this fairly easily by differentiating the first equation, rearranging, and removing one of the variables, which gives me a...

Homework Statement show that the general solution of the differential equation d^2/dt^2 + 2 *alpha * dr/dt + omega^2 * r = 0, where alpha and w are constant and R is a function of time "t" is R = e^(-alpha * t) * [ C1*sin( sqrt(omega^2 - alpha^2) * t) + C2*cos( sqrt(omega^2 - alpha^2) * t)...

Homework Statement Why do we need two solutions to solve a 2nd order linear differential equation? lets consider a differential equation with equal roots for auxiliary equation. So the reasoning behind why can't we use y=Aen1x+Ben2x as its general solution is because since the roots are equal...

Hi,I need help please, i want to know how to solve de differential equation of a system of two degree of freedom using eigenvalues or eigenvectors or if I can use any another way to solve this kind of equations.

what is a good book to learn first order differential equations ??

what is a good book to learn first order differential equations ??

i have few doubts about differential equations and numerical methods ... in a differential equation question ... you are given an instantaneous rate of change... and you are supposed to find the function that gives , this instantaneous rate of change is this same as ... f(0)=1...

consider ODE : Show that the solution to this ODE is: Can someone tell what kind of ODE is it?I thought,it's on the form of Bernoulli ODE with P(x)=0.Is it possible to still solve it by using Bernoulli Methodology?I mean by substituting u=y^1-a with a=2? Thanks

Given a system of linear differential equations $$x_{1}'=a_{11}x_{1}+a_{12}x_{2}+\cdots a_{1n}x_{n}\\ x_{2}'=a_{21}x_{1}+a_{22}x_{2}+\cdots a_{2n}x_{n}\\ \ldots\\ x_{n}'= a_{n1}x_{1}+a_{n2}x_{2}+\cdots a_{nn}x_{n}$$ this can be rewritten in the form of a matrix equation...

So I ran into an case I have not seen before. Say we have a system of 3 equations such that W´=AW, where W=(x(t),y(t),z(t)) and A is a 3x3 matrix. The way I usually approach these is by finding the eigenvalues of A to then find the eigenvectors and thus find the ¨homogenous¨ solution. What...

Hi members, Laplace transform using differential equations.(see attached PDF file) My question d/ds(s^2 y- s Y(0)-Y'(0).)... Y(t)=sin(sqrt(t)) Y(o)=0 Now Y'= cos(sqrt(t)/2sqrt(t) Y'(0)=infinity d/ds (Y'(0)=?? can it be treated as a constant or can we change limit and differentiation??I...

Could someone explain under which principle does Skinner's machine operate? Is it just a free falling mass that's taken back to it initial position by very little input energy, thus generating a constant gradient or potential difference, and generating energy, or is it just storing kinetic energy?

Could someone tell me an application of the model of free fall to industry or more generally by using Newton's second law and the law of gravitation, construct a model similar to the free fall one, that has an application in industry

i have a few questions to ask about differential equations ... how many types of differential equations are there ... ? sometimes i like to make up themes for my studies ... few funny things went through my head ...when i saw this thread ,How is it that mathematics describe reality so well? i...

I'm trying to find the distribution of a random variable ##T## supported on ##[t_1, t_2]## subject to ## \mathbb{E}[V(t', T)] = K, \forall t' \in [t_1, t_2]##. In integral form, this is : $$ \int_{t_1}^{t_2} V(t', t).f(t) \, dt = K,\forall t' \in [t_1, t_2], $$ which is just an exotic integral...

Homework Statement Compute the convolution f*g for the given function f and g. f(t)=cost g(t)=U2(t)Homework Equations f*g=∫f(t-u)g(u)du The Attempt at a Solution So I pretty much only know how to plug in the functions into the integral for convolutions. Not really sure how to evaluate it...

Homework Statement Get the two stationary points for the equation ## y= ((ln x)^2)/x ## Homework EquationsThe Attempt at a Solution i have managed to solve ##dy/dx=((2xlnx/x- (ln x)^2))/x^2 = 0, ln x(2-ln x) = 0, x= 1, x =e^2##

DE= Differential equations. There is an Encyclopedia of Integer Sequences for example, but I am not able to find the equivalent for DE. I would like to find a list with all the differential equations that have been solved up to date. A website or any other source would be interesting. If the...

I took differential equation 2 last semester and the book we used wasn't so great at explaining a lot of things. I was wondering if anyone knew of a video lecture series that parallels my book (Differential Equations 4th Ed. by Blanchard, Devaney, and Hall). Specifically I am having trouble with...

Hi, Is there a proof that complex replacement is a valid way to solve a differential equation? I'm lacking some intuition on the idea that under any algebraic manipulations the real and imaginary parts of an expression don't influence each other. For example, if I'm given: $$p(D) x = cos(t)$$...

Homework Statement I want to solve this systemx' = \left( \begin{array}\\ 7 & 1 \\ -4 & 3 \end{array} \right)x + \left( \begin{array}\\ t \\ 2t \end{array} \right) Homework EquationsThe Attempt at a Solution i found the eigenvalues to both be 5. The eigenvector is (1,-2) and the generalized...

Quick question, can you solve non-homogeneous systems with repeated eigenvalues the same ways? i.e. variation of parameters, undetermined coefficients, etc... would the fundamental matrix contain the solution with the generalized eigenvalue? Thanks!

I'm pretty rusty at calculus. I did well in them, but my memory is terrible and I have forgotten a lot. I'm going to take ordinary differential equations (it looks and sounds like an intro DE class with some linear algebra too) next spring. What should I study and what not to prepare for this...

Homework Statement A metal sphere is subjected to a heat flux, 5000 W/m2. It is originally at 20 C. How long does it take to heat to 90 C? D = 5 cm density = 8522 kg/m3 cp = 0.385 kJ/kg-K k = 104 W/m-k Homework Equations rate of heat input = rate of heat accumulation -k*A*dT/dr = m*cp*dT/dt...

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 The problem is in the picture. #17 I would have typed it but there are graphs that are needed for solving it. Basically trying to figure out which y(t) graph belongs to one of the sinusoidal forced equations with various parameters. Homework Equations euler's formula...