let-g-x-x-1-x-2-1-prove-that-g-is-solution-for-the-differencial-equation-4-1-x-2-y-4xy-y-0-prove-that-g-is-C-on-R-2-determine-a-relation-between-g-n-0-and-g-n-

Tinku Tara June 4, 2023 Differentiation 0 Comments

Question Number 40103 by maxmathsup by imad last updated on 15/Jul/18

let g(x)=(√(−x+(√(1+x^2 )))) 1) prove that g is solution for the differencial equation 4(1+x^2 )y^(′′) +4xy^′ −y =0 .prove that g is C^∞ on R 2) determine a relation between g^((n)) (0) and g^((n+2)) (0)

$${let}\:{g}\left({x}\right)=\sqrt{−{x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }} \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{g}\:{is}\:{solution}\:{for}\:{the}\:{differencial}\:{equation} \\ $$$$\mathrm{4}\left(\mathrm{1}+{x}^{\mathrm{2}} \right){y}^{''} \:+\mathrm{4}{xy}^{'} \:−{y}\:=\mathrm{0}\:\:\:.{prove}\:{that}\:{g}\:{is}\:{C}^{\infty} {on}\:{R} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{a}\:{relation}\:{between}\:{g}^{\left({n}\right)} \left(\mathrm{0}\right)\:{and}\:{g}^{\left({n}+\mathrm{2}\right)} \left(\mathrm{0}\right) \\ $$

Facebook Tweet Pin

let-g-x-x-1-x-2-1-prove-that-g-is-solution-for-the-differencial-equation-4-1-x-2-y-4xy-y-0-prove-that-g-is-C-on-R-2-determine-a-relation-between-g-n-0-and-g-n-

Leave a Reply Cancel reply