# Tagged Questions

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

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### ODE Hyperbolic fixed point study

Here is a problem I can not solve : Let $X(x, y)$ be a $C^{\infty}$ vector field defined on $\mathbb{R}^2$ such that $X(x, y) = (y + a(x, y), x+ b(x, y))$ where $a, b : \mathbb{R}^2 \to \mathbb{R}$ ...
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### Transform the equation using a substitution

I'm trying to rewrite this equation: so that it's in the diffusion equation form:
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### Door mechanism differential equation

I have been wondering about a door mechanism I have seen. It has a wire attached to the upper corner of the door and from there to the corresponding corner in the door frame, where a weight hangs from ...
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### For which value of $r$ is the nonlinear dynamical system dissipative?

I could really use some help with the following: When I have input $u$ and output $y$ of the following nonlinear dynamical system, How can I determine for which values of $r$ this system will be ...
let $r(θ)=a(1-β^2)/(1+β\cos\theta)$ representing the distance from the Sun to a planet. With $0<β<1$, show that the orbit represented by this function $r(θ)$ is an ellipse described by $(x+\sqrt{... 2answers 20 views ### Why is the solution to this ODE as follows?$rV = \pi x − f + \mu x \frac{\partial V(x)}{\partial x} + 0.5\sigma^2 x^2 \frac{\partial^2 V(x)}{\partial x^2}$Why is the general solution given by:$V(x) = A_0 + A_1 x + A_2 x^\lambda + A_3 x^\...
$T = \frac{1}{2}M_{w}\dot{x}^{2} + \frac{1}{2}I_{w}\frac{\dot{x}^2}{r^2} + \frac{1}{2}M_{b}((\dot{x} + l\dot{\theta}cos(\theta))^2 + (l\dot{\theta}sin(\theta))^2) + \frac{1}{2}I_{b}\dot{\theta}^{2}$ \$...