Question

What are the degree and order respectively of the differential equation satisfying $e^{y\sqrt{1-x^2}+x\sqrt{1-y^2}}=c{e}^x$, (where c > 0, |x| < 1, |y| < 1)?

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

Answer 1

The correct option is A 1, 1

Given equation is $e^{y\sqrt{1-x^2}+x\sqrt{1-y^2}}=c{e}^x$

$⟹\frac{e^{y\sqrt{1-x^2}+x\sqrt{1-y^2}}}{e^x}=c$

Differentiating with respect to $x$ elimiates the constant $c$,

$\therefore$ the order of the differential equation is $1$,