If from the derivate, we can generate an equation that is the equation of the tangent straight, so:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=\frac{\mathrm{d} y}{\mathrm{d} x}[/tex]

[tex]\mathrm{d} y=\frac{\mathrm{d} y}{\mathrm{d} x}\mathrm{d} x[/tex]

[tex]y=\frac{\mathrm{d} y}{\mathrm{d} x}\mathrm{d} x+y_{0}[/tex]

[tex]y(x)=y'(x_0)(x-x_0)+y(x_0)[/tex]

And this extends even to other cases...

[tex]y(x)=y''(x_0)\frac{(x-x_0)^2}{2}+y'(x_0)(x-x_0)+y(x_0)[/tex]

[tex]y(x)=y^{**}(x_0)^{\frac{(x-x_0)^2}{2}}\times y^{*}(x_0)^{(x-x_0)}\times y(x_0)[/tex]

Being

[tex]y^{*}(x)=exp\frac{f'(x)}{f(x)}[/tex]

The geometric derivate

... So, similarly, is not possible to generate a characteristic equation with integration?

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# Integral's equation

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