What are the degree and order respectively of the differential equation satisfying `e^(ysqrt(1-x^2)+xsqrt(1-y^2)) =ce^x`

Options

A. 1,1
B. 1,2
C. 2,1
D. 2,2

Answer

A

Explanation

`e^(y(sqrt(1-x^(2)) +xsqrt(1-y^(2))-x=c)`
` Rightarrow ysqrt(1-x^(2)) +x (sqrt(1-y^(2)) = log c`
` (dy)/(dx) sqrt(1-x^(2)) +y . 1/(2sqrt(1-x^(2))) (-2x)+ Sqrt(1 -y^(2))`
` +x 1/(2sqrt(1-y^(2)) (-2y) .(dy)/(dx) -1=0`
` Rightarrow (dy)/(dx) sqrt(1-x^(2)) - (xy)/(sqrt1-x^(2)) +sqrt(1-y^(2)) - (xy)/(sqrt(1-y^(2)) .(dy)/(dx) =1`
degree =1, order=1