Let y=y(x) be the solution of the differential equation xdy-ydx=x2-y2dx, x≥1, with y(1)=0. If the area bounded by the line x=1,x=eπ,y=0 and y=y(x) is αe2π+β, then the value of 10(α+β) is equal to ___ .

Question

Let

y = y (x)

be the solution of the differential equation

x d y - y d x = \sqrt{(x^{2} - y^{2})} d x, x \geq 1

, with

y (1) = 0

. If the area bounded by the line

x = 1, x = e^{π}, y = 0

and

y = y (x)

α e^{2 π} + β,

then the value of

10 (α + β)

is equal to ___ .

Correct Answer

Please login to view the detailed solution steps...