Tagged Questions

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

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Heat Ecuation : Exchange partial derviate and series

I'am having a problem when checking the validity of the solution i found for the heat ecuation: \begin{cases} U_{t}(x,t)=U_{xx}(x,t),\ {(x,t)\in (0,1)\times(0,+\infty)} \\ U(x,0) = x^2 - x\\U(0,t)=0\...
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Polar coordinates for vector field to find sticking flow

I am currently working on an impacting system which is basically just a spring damper and a circular enclosure. Because of the rotational symmetry of the problem I need the vector field in polar ...
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How small need it be to approximate integral as one area of product of initial value times length.

$$\left(\int_{t}^{t+\Delta t}a(t')dt'\right), a(t) \text{ is scalar}$$ How small need $\Delta t$ be to approximate $$\left(\int_{t}^{t+\Delta t}a(t')dt'\right)$$ as $$a(t)\Delta t$$ [ Just one ...
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Development of Calculus and differential equation question

In my post Showing propagation in ordinary differential equation, I have a hard time getting the exponential solution of propagation$$y(t+\Delta t) = e^{- \int_{t}^{t+\Delta t}H(t')dt'}y(t)$$. I now ...
I have a very simple linear First Order Homogeneous Differential Equation with time but this makes me ponder upon the definition of derivative and integral. $$\frac{dy}{dt} = -H(t)y$$ where $y, H(t)$ ...