Find the specific solution of the differential equation dy dx equals the quotient of 3 times y and x square with condition y(-3) = e

Question

Find the specific solution of the differential equation  with condition y(-3) = e

A
B
C
D	None of these

Answer 1

This is an easy separation of variables differential equation. Rewriting

dy/y = 3dy/(x²)

Integrating both sides

∫dy/y = 3∫dy/(x²)

ln(y) = -3/x + C₁

Take both sides to the power of e

e^ln(y) = y = e^-3/x+C = e^Ce^-3/x = Ke^-3/x where K is just another constant = e^C

It was given that y(-3) = e

Ke^-3/-3 = Ke = e --> K = 1

y = e^-3/x

Checking

dy/dx = 3/(x²)e^-3/x = 3y/x²