# Questions tagged [differential]

For question about the differential of a map from an open set of a vector space to a vector space.

837 questions
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### Eigenvalues of differential equation are sines of integers times a constant

We know of differential equations whose eigenvalues are integers "m". Can anyone point to a differential equation whose eigenvalues are terms of the form $\sin(ma)/\sin(a)$, which reduces to integers ...
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### Differential geometry and frenet formula

Given a curve C by its arclenght (vector $r(s)$), prove that $\frac{dT(s)}{ds} \times \frac{d^2 T(s)}{ds^2} = k^2 \omega$ where k is the curvature and $\omega$ is the darboux vector. I tried using ...
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### Use Duhamel's principle in PDE

Let $u(t,x)$ be solution for: $$u_{tt}-u_{xx}=q(t,x)u$$ with zero initial conditions. If $q$ is bounded in $\mathbb{R}^2$, show that $u \equiv 0$ using Duhamel's principle
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### Integrating Factor Techniques for Exact ODE

As explained in this answer, an inexact ODE in the form $M(x,\ y)\ dx + N(x,\ y)\ dy = 0$ can be transformed into an exact ODE via multiple integrating factors which vary from each other non-trivially ...
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### Differential Equation with arctanx

I have a separable equation $\frac{dy}{dx}$=$\frac{27}{y^{1/3}+81x^2y^{1/3}}$ I separated both sides by multiplying by dx and factoring out the y^{1/3} and ...
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### Equations of Motion in Cylindrical Co-ordinates

I've run into an interesting set of differential equations, that I'm not 100% sure where to begin- I'm not looking for a 100% complete solution, more just a push in the right direction of where I can ...
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### Finding a Linear Second Order Differential Equation $F(x, y, y', y'') = 0$ for which $y = c_1x + c_2x^3$ [closed]

Find a linear second-order differential equation $F(x, y, y', y'') = 0$ for which $y = c_1x + c_2x^3$ is a two-parameter family of solutions. Make sure that your equation is free of the arbitrary ...
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Is there somebody who can help me to find a solution for $$\begin{cases} y^i\frac{\partial b(x,y)}{\partial x^i}=0\\ y^i\frac{\partial b(x,y)}{\partial y^i}=b\\ \end{cases}, b:R^{2n}→R, x=(x^1,…,x^n)\... 1answer 21 views ### Existence of solutions for an Ordinary differential equation modelling a real physical problem [closed] Does an ODE (or Initial value problem) modelling a real physical problem always have a solution, whatever the initial conditions? If so, can this be extended to Partial differential equations as well? 1answer 51 views ### Differentials and Integration I have been informed that consecutive differentials in iterated integral problems are actually connected via the exterior product. So the factor dx\ dy in \int\int x^2\ dx\ dy is actually the ... 1answer 26 views ### Lipschitz Continous Function and Differentiable. Does this imply it derivative is bounded? While studying differential equations, I came across the existence and uniqueness of solutions for a differential equation. Then after studying some theorems these statements are troubling me. Let f:... 1answer 45 views ### condition for one-form to be exact differential Simple question I suppose: Having a (smooth) one-form$$\omega=\omega_i dx^i\in \Lambda(M)$$Is there a test to find out if \omega is exact differential? Or more precisely that there exists a ... 1answer 39 views ### Computing the differential of a Lie group action (Ex. 27.4 page 252 Loring Tu) (The differential of an action). Let \mu: P \times G \rightarrow P. For g \in G, the tangent space T_gG may be identified with l_{g*} \mathfrak{g} , where ... 2answers 50 views ### Differential Equation help me solve Help me solve this Differential Equation?$$y\cdot y''+(y')^2=2x1answer 50 views ### Solve this differential equation dy/dx [closed] Solve this differential equation where 0answers 30 views ### Finding a curve orthogonally equidistant between two curves. I have two curves, f_1(x) and f_2(x) which meet at (x_0, 0) and (x_1, 0), these curves as such form a closed shape, but not necessarily a convex one. I would like to generate a curve f_c(x) ... 0answers 49 views ### derivative exist almost everywhere I am working on a problem finding an error of an example that uses integration by parts. The condition of the example says that f' and g' exist almost everywhere. If f' and g' exist almost ... 1answer 21 views ### SVM “kernel trick” and linearly separable sets of points Background info: in Machine Learning there's something called an SVM (Support Vector Machine) that employs a "kernel trick" to map sets of points to a higher dimension in order to find a hyperplane ... 0answers 30 views ### Find a gradient system admitting a given solution Consider the Gradient Dynamical System, \begin{align*} \begin{cases} \dot{\gamma}(t)=-\nabla f(\gamma(t)),t>0,\\ \gamma(0)=x_0\in\mathbb{R}^n. \end{cases} \end{align*} We all know that if f is C^... 0answers 22 views ### Algebraic Groups, dual numbers and differentials I was looking for a method to compute the explicit differential of a regular map between algebraic groups. More precisely if X is a sub-variety in an algebraic group G (say over a finite field k)... 1answer 11 views ### Bernoulli differential equation alike I am quite new to differential equations and I have the following \partial u(x)/\partial x = a(x)u(x)^2+b(x)u(x)+c(x)  which is, to the best of my knowledge, not exactly a Bernoulli differential ...
The function is $G(x,y)= 1$ if $y \neq e^{x}$ and $0$ if $y= e^{x}$.