Difference between revisions of "Abel dynamic equation"
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| + | Let $\mathbb{T}$ be a [[time scale]] and let $f_i,g_k \colon \mathbb{R} \rightarrow \mathbb{R}$ for $i=0,1,2$ and $k=0,1$. The Abel dynamic equation of the second kind is | ||
| + | $$\left[ g_0(x)+g_1(x) \left( \dfrac{u+u^{\sigma}}{2} \right) \right]u^{\Delta} = f_0(x)+f_1(x)u+f_2(x)u^2.$$ | ||
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| + | =Properties= | ||
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=References= | =References= | ||
[http://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=7913&context=masters_theses Abel dynamic equations of the first and second kind] | [http://scholarsmine.mst.edu/cgi/viewcontent.cgi?article=7913&context=masters_theses Abel dynamic equations of the first and second kind] | ||
Latest revision as of 19:28, 5 April 2015
Let $\mathbb{T}$ be a time scale and let $f_i,g_k \colon \mathbb{R} \rightarrow \mathbb{R}$ for $i=0,1,2$ and $k=0,1$. The Abel dynamic equation of the second kind is $$\left[ g_0(x)+g_1(x) \left( \dfrac{u+u^{\sigma}}{2} \right) \right]u^{\Delta} = f_0(x)+f_1(x)u+f_2(x)u^2.$$
