Question

Equation of curve through point (1,0) which satisfies the differential equation (1 + y)2dx - xydy = 0, is

• A. $x^{2} + y^{2} = 1$
• B. $x^{2} - y^{2} = 1$
• C. $2x^{2} + y^{2} = 2$
• D. None of these

Answer 1

Answer: (B)

$x^{2} - y^{2} = 1$

Answer 2

We have $\frac{dx}{x} = \frac{ydy}{1 + y^{2}}$

Integrating, we get log $|x| = \frac{1}{2}\log(1 + y^{2}) + \log c$

or $|x| = c\sqrt{(1 + y^{2})}$

But is passes through (1,0 ), so we get c = 1

$\therefore$ Solution is x2 = y2 + 1 or x2 - y2 =