# Tagged Questions

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### Linearize a first order differential equation

The system described by $x'=2x^2-8$ is linearized about the equilibrium point -2. What is the resulting linearized equation? Answer is $x'=-8x-16$. How? I have no idea how it went from the first ...
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### solving the equation

let there be a function $f(x)= \ln x-kx^2, k>0$ determine for whihc values of $k$ ,the equation $f(x)=0.5$ has a single solution; attemp to solve: $$0.5 = \ln x-kx^2$$ $$kx^2 +0.5 = \ln x$$ ...
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### I need help figuring this error percentage homework problem.

Question: Government economists in a certain country have determined that the demand equation for soybeans is given by $p = f(x) = \frac{55}{2x^2 + 1}$ where the unit price p is expressed in dollars ...
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### How to go about solving this question on differentials?

A ring of a planet has an inner radius of approximately 52,000 km (measured from the center of the planet) and a radial width of 19 km. Use differentials to estimate the area of the ring. (Round ...
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### Modeling salt and water with differential equations

From Differential Equations (Blanchard, Devaney, and Hall, page 35). My question is about the model. I let $x$ be the amount of salt and $t$ the minutes passed. Then ...
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### Differential equation $\frac{dy}{dt}=y(1-y)$

I'm starting with $$\frac{dy}{dt}=y(1-y)$$ Then I take the obvious steps. ...
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### Every equation of the form $ax''+b(x^2-1)x'+cx=0$, $a,b,c>0$ can be transformed into Van der Pol's equation

Show that every equation of the form $$ax''+b(x^2-1)x'+cx=0,$$ $a,b,c>0$ can be transformed into Van der Pol's equation by a change in the independent variable. I am unable to find this ...
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### Fourier transform help for solving $u_t+u_{xxxx}+u_{xx}=0$

I just started to learn a little bit of fourier analysis in solving PDEs. I want to find a solution $u(x,t)$ to $u_t+u_{xxxx}+u_{xx}=0$. My attempt: Applying the fourier transform to both sides gives ...
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### Finding functions in a differential equation that satisfies two solutions

"Given a differential equation of the form $a(x)y''+b(x)y'+y=0$, find functions $a(x)$ and $b(x)$ so that $y=x$ and $y=x^2$ are each a solution of this differential equation." I'm really not sure how ...
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### if $X$ is a vector fild in $\mathbb{R}^3$ and $h$ is a periodic orbit, then $X$ have a singularity? [duplicate]

if $X$ is a vector fild in $\mathbb{R}^3$ and $h$ is a periodic orbit, then $X$ have a singularity? and in dimension $n$? I know there is singularity when $n=2$.
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### Find eigenvalues and eigenfunctions of this BVP: transforming the eqn?

so I've been stuck on this problem after my first attempt. I got the trivial solution after using the characteristic equation $3r^2 - 4r + 1 = 0$... Find all eigenvalues and associated eigenfunctions ...
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### If $p$ is a regular point $X$ such that $p \in \omega(p)$ then $\omega(p)$ is periodic orbit. [closed]

Let $X$ be a field in $\mathbb{R}^3$, $C^1$ class. If $p$ is a regular point $X$ such that $p \in \omega(p)$ then $\omega(p)$ is periodic orbit.
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