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Results tagged with ca.classical-analysis-and-odes
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user 116983
Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.
2
votes
1
answer
191
views
A first order ODE problem
Fix $a>0$ and $b>0$. Does the following ODE
\begin{equation}
G(x)^2+2axG(x)G'(x)+2aG'(x)(x-b)=0 \tag{*}
\end{equation}
have a solution, say, $F(x)$, that satisfies $F(x)>0$ and $F'(x)<0$ on $(b,\inft …
- 389
12
votes
1
answer
351
views
A problem involving the Error Function
I am looking at the following function on the domain $x\geq 0$:
$$F(x)=(x+a)e^{x^2}(1-\mathrm{erf}(x))-\frac{b}{\sqrt\pi},$$
where $a>0$, $0<b<1$ are parameters. From plotting this function for diff …
- 389