Find the general solution of the following differential equation: e^x √{1 - y^2}dx + y/x dy = 0 ​

Question

Find the general solution of the following differential equation:

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

Answer 1

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

Integrating,

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

Consider the integral ∫e^x. x dx

By ILATE rule,

Therefore the solution of the given differential equation is

e^x(x - 1) - \(\sqrt{1-y^2}\) = c