Prove-that-X-t-1-1-t-2-LN-1-1-t-2-t-Y-t-t-1-t-2-function-is-the-solution-of-the-following-equation-y-1-y-2-y-

Question Number 181751 by Shrinava last updated on 29/Nov/22

Prove that,

{\begin{cases} X (t) = \frac{1}{\sqrt{1 + t^{2}}} - LN \frac{1 + \sqrt{1 + t^{2}}}{t} \\ Y (t) = \frac{t}{\sqrt{1 + t^{2}}} \end{cases}

function is the solution of the following

equation :

y \sqrt{1 + y^{' 2}} = y^{^{'}}