# Tagged Questions

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### Insightful books on differential equations?

What are some recommendations for insightful books on differential equations and difference equations? These books don't need to be in the format of a textbook, and don't need to provide the same ...
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### What are the complex solutions of a linear homogenous ODE of order $n$ with constant coefficients?

What are the complex solutions of a linear homogenous ODE of order $n$ with constant coefficients? Where can I read a proof? p.s. I don't even see the answer to the first question with a google ...
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### Reference Request for Linear ODEs

Homogeneous, linear ODEs of the form $$\mathrm{f}^{(n)}(x)+a_{n-1}\mathrm{f}^{(n-1)}(x)+\cdots+a_1\mathrm{f}'(x)+a_0\mathrm{f}(x)=0$$ where each $a_i \in \mathbb{R}$ are known to have "solution ...
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Let's have ode $x' = f(x)$, $f(0) = 0$, $x\in \mathbb{R^n}$. There is clasical theorem that states that if all eigenvalues of ${\rm Df}(0)$ have nonzero real part, than $x'=f(x)$ and $x'={\rm Df}(0) ... 1answer 60 views ### Reducing size of ODE system by using symmetries: examples, references help request. We know: A high order differential equation can be expressed as an ODE system. Knowledge of a symmetry allow one to reduce the order of a differential equation. So if we do$n$-order ODE ... 1answer 85 views ### Good ODE Books That Explain How Solution Methods Came To Be and Their Justifications As part of the mathematics program offered at my college, I took an introductory ODE course a few semesters back. This was the one math course in my entire college career that I was totally lost in. ... 1answer 52 views ### ODE system and single PDE “equivalence”, reference request The answers to this question Replacing large-dimensional ODE systems with one PDE suggest that, in general, one can not hope for "replacing" an ODE system with a single PDE. On the other hand, this ... 4answers 161 views ### Pde book suggestion. I am studying PDE. And I want to know introduction to PDE book's names, which contain direclet problem, Sturm liouville problems, cauchy problems, euler, eigen functions and like this. But the ... 2answers 177 views ### Wave-Particle Duality in PDE? I am reading Arnold's Lectures on Partial Differential Equations. It is definitely a good book, yet sometimes I am a little bit confused. One theme of the first chapter seems to be From the ... 2answers 116 views ### Ideas about an Ordinary Differential Equations research work (University level) Good afternoon to everyone, I need some ideas about a Ordinary Differential Equations research work. It is for the ODE subject that I am doing at my Mathematics degree in my University. They asked me ... 1answer 64 views ###$\dot y=y^2-t$Differential Equation Liouville proved that the differential equation$\dot y=y^2-t$does not have a solution in form of algebraic equations. Do you know any reference where I can find the proof for that? 1answer 47 views ### References about non uniqueness of solution in ordinary differential equations I am looking for some example of IVP with non unique solution. I already know the examples of$f(x,y)=k\sqrt{y}$and$f(x,y)=k y^{2/3}$. Any book or link is welcome. 1answer 43 views ### Existence of solutions to linear evolution equation with a noncoercive operator Consider the Gelfand triple$V\hookrightarrow H \hookrightarrow V'$and, for given$T>0$, the Sobolev-Bochner space $$\mathcal W(0,T) := \{ v \in L^2(0,T;V): \dot v \in L^2(0,T;V')\}.$$ Consider ... 2answers 76 views ### Book searching in Elliptic Equation I am learning a course with the subject of Elliptic Equations. If you know about it, please recommend me a book on Elliptic Equations. And if that's possible, someone post these books/author/...that ... 0answers 107 views ### Monodromy Groups of Differential Equations I have heard that monodromy groups and analytic continuation can be used to construct new solutions to a differential equation from a particular solution. What references (textbook, or papers) could I ... 1answer 116 views ### good textbook to self-learn systems of ODEs I've taken regular Ordinary Differential Equations. Right now I'm taking Systems of ODEs and the textbook is less than stellar. I was wondering if anyone could point me to a decent self-study book for ... 1answer 35 views ### German Books in Qualitative ODE? Can anyone refer to me some good german books on introductory, qualitative ODE that cover topics like Picard-Lindelof, Peano's Existence Theorem? 0answers 72 views ### Is there a generalization of the ODE Comparison Theorem to n dimensional systems such as this one? Is the following theorem true? If so, under what conditions? If not, why not? For any finite set of points$S$, let$conv(S)$denote the convex hull of$S$. Let$f:\mathbb{R}^{n+1} \to \mathbb{R}^n ...
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I'm looking for references (books or pdf) about the following themes (especially the first two) : Fourier Series of Distributions. Distributional solutions of ordinary differential equations. ...
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### A method called “incorrect method”

Good night. Is there a method called "incorrect method" to calculate second order differential equations? If so, please, is there a web page about it, as I have to investigate this method? Thank ...
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### Dynamical systems and differential equations reviews/surveys?

I would be very glad if someone could point me to modern reviews/surveys on these topics. To be concrete, I'll provide some examples: S. Smale, Differentiable dynamical systems D. V. Anosov, On the ...
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### Inverse problem in calculus of variations

I am interested in knowing which differential equations follow from a variational principle. I am reading this and it provides the answer for ordinary differential equations. Is there a complete ...
I need to find the solution of the IVP $$\frac{dp}{dt}=ap-bp^2, p(0)=p_0$$ where $a,b$ are constants. I have found $$p(t)=\frac{ap_0}{bp_0+(a-bp_0)e^{-at}}$$ Now if $p(t_1)=p_1$ and $p(t_2)=p_2$ ...
During my research I came across a weak gronwall-type inequality of the following type: $$-\int_0^T f'(t)(u(t)-u_0) \leq \int_0^T f(t)u(t)$$ for non-negative $f\in C_c^\infty(0,T)$, $u\in L^1(0,T)$ ...