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Sep
10
comment Solution of a differentiation in integral form
@ComplexGuy When $t=0$, $\sin(\omega t) = 0$, and the equality follows.
Sep
10
revised Comparison between Bessel's coefficients
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Sep
10
answered Comparison between Bessel's coefficients
Jul
22
comment Perturbation Theory on Finite Domains
You should read about the WKB approximation. A great treatise on the asymptotics of $y'' + p(x) y = 0$ can be found in chapter 6 of Olver's Asymptotics and Special Functions.
Jul
14
comment Nonlinear equation (oscillon) comparison
@ComplexGuy en.wikipedia.org/wiki/Virtual_work
Jul
13
revised General Solution of a Differential Equation using Green's Function
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Jul
13
revised General Solution of a Differential Equation using Green's Function
added 3 characters in body
Jul
13
revised General Solution of a Differential Equation using Green's Function
added 3 characters in body
Jul
13
answered General Solution of a Differential Equation using Green's Function
Jul
12
revised Proving a triangle is a right triangle given vertices, using vector dot product
edited tags
Jul
12
comment Solve the following differential equations by converting to Clairaut's form through suitable substitutions.
@Vish.Math See my last edit but be warned that there is never a satisfactory explanation for intuitive steps. Math is experience.
Jul
12
revised Solve the following differential equations by converting to Clairaut's form through suitable substitutions.
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Jul
11
answered Black Scholes Merton PDE with a time variant boundary condition
Jul
11
comment Black Scholes Merton PDE with a time variant boundary condition
A few questions: Is there a relationship between $r$, $\delta$ and $\sigma$? Are all constants positive? One bigger than the other, etc? What's the domain for $V$? What's the behavior you're expecting for $S$ as the price $V$ goes to infinity?
Jul
9
revised Is this function bounded? Next question about integral $\int_{\partial M} \frac{1}{||y-x||} n_y \cdot \nabla_y \frac1{||y-x||} dS_y$.
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Jul
9
comment Solution of a differentiation in integral form
@ComplexGuy Nope, the definition of Spherical Bessel functions is \begin{align}j_n(x) &= \sqrt{\frac{\pi}{2 x}} J_{n + \frac{1}{2}}(x) \\ \\ y_n(x) &= \sqrt{\frac{\pi}{2 x}} Y_{n + \frac{1}{2}}(x)\end{align}
Jul
8
answered Is this function bounded? Next question about integral $\int_{\partial M} \frac{1}{||y-x||} n_y \cdot \nabla_y \frac1{||y-x||} dS_y$.
Jul
8
comment How to find out where a solution to a differential equation is defined?
The answer to your question is that theorem. Any ODE book will have a detailed proof, along with the relation between existence, uniqueness and continuation of solutions depending on parameters and initial conditions.
Jul
8
comment Ordinary Differential Equations - Sturm Liouville
Hint: Sturm separation theorem
Jul
8
revised How to find out where a solution to a differential equation is defined?
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