# Tagged Questions

Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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### Differentiation calculation

$L(E)$ espace fonction continuous and linear $$\begin{array}{llll} \psi:& L(E)\times E&\longrightarrow& E\\ &(u,x)&\longrightarrow &u(x) \end{array}$$ proved the application ...
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### Preparations to finals, validation needed

I have an exam in a few days from now and I'm very nervous. I tried to tackle this one with all I got, but I'm not sure if I'm correct. If anyone can direct me, and tell me if and where I'm doing ...
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### Choose Scaling for t

My question is the last part of the d) part of the exercise 1.17 in Mark Holms' Introduction to Applied Mathematics. The exercise is given below, where I have emphasized the part of it that is my ...
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### Sturm-Liouville eigenvalue problem of order 4

I want to solve the eigenvalue problem $W''''=\lambda W$ with the boundary conditions $W(0)=W'(0)=W(l)=W'(l)=0$. Has someone a hint how to solve that? Thank you...
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### Phase line and Equilibrium Points

Consider the differential equation $dy/dt=y^8+3y^6-y^2-1$. Sketch the phase line and classify the equilibrium points. Since when $y=0$, the derivative is negative and when $y>1$ the derivative ...
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### Non-Conservative System

I'm having a bit of trouble understanding the concept of a conservative system mathematically. A problem in a textbook (Arnold's Mathematical Methods for Classical Mechanics) is asking me to give an ...
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### Make mathematical sense of the Dirac well Potential Equation

A classical problem in quantum mechanics involving the Dirac Delta function is given by $$y''+(\delta(x)-\lambda^2)y=0$$ Then, to find ''bound states'', you solve on the right and find the ...
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### Regarding continuity and the value of the function at the point of discontinuity.

Suppose while solving a boundary value problem, we have a two piece solution $f_1(x)$ and $f_2(x)$ where $f_1(x)=f(x)$ for $x < x_0$ and $f_2(x) = f(x)$ for $x>x_0$. If there is a matching ...
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### How do you read a partial differential equation?

In calculus we can read the "normal derivative", $\frac {df}{dx}$, as the rate of change of our function $f$ with respect to $x$. With partial derivatives of multivariate functions it is very much the ...
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### Finite Difference for Hamilton-Jacobi-Bellman without boundary conditions

Let $t\in\mathbb{R}_+$ denote time, $x \in X$ is the state and $u \in U$ the control. The objective function is $F:X \times U \to\mathbb{R}$ and $f:X \times U \to\mathbb{R}$ is the law of motion for ...
Second order linear differential equation is given below. $y''+\frac{2}{x}y'+k^2y=0,$ where $k$ is constant and $x\neq 0$ I already know that the basis are $y_1=\frac{e^{-ikx}}{x}$ and \$y_2=\frac{e^...