Let y = y(x) be the solution of the differential equation e^x √1-y^2dx+(y/x)dy = 0, y(1) = -1. Then the value of [y(3)]^2 is equal to:

Question

Let y = y(x) be the solution of the differential equation e^x \(\sqrt{1-y^2}\) dx+(y/x)dy = 0, y(1) = -1.

Then the value of [y(3)]² is equal to:

(1) 1 - 4e³

(2) 1 - 4e⁶

(3) 1+4e³

(4) 1+4e⁶

Answer 1

Answer is: (2) 1 - 4e⁶