Find the particular solution of the differential equation e^x √(1 -y^2) dx + y/x dy = 0,

Question

Find the particular solution of the differential equation

e^x\(\sqrt{1-y^2 dx} + \frac{y}{x}\) dy = 0,

given that y = 1, when x = 0.

Answer 1

Given, differential equation is

Also, given that y = 1, when x = 0

On putting y = 1 and x = 0 in Eq, (i), we get

\(\sqrt{1-1}\) = 0 - e⁰ + C

⇒ c = 1 [∵ e⁰ = 1]

On substituting the value of C in Eq. (i), we get

\(\sqrt{1-y^2}\) = xe^X - e^x + 1

which is the required particular solution of given differential equation.