Which of the following is a separable, first-order differential equation?

Question

A) dy/dx= x+y/2x
B) dy/dx=x+y/x-y
C) dy/dx=sinx <<
D) dy/dx=xy/x+y
E) dy/dx= 2lnxy

2) The differential equation dy/dx=y/x^2 has a solution given by:
A) y=C sqrt(x^2+4)
B)y=C e^-1/x
C)-1/2ex^2+C
D) x^2+y^2=C
E)y=Ce^-kt

Answer 1

#1 ok

#2
dy/y = dx/x^2
lny = -1/x + c
y = e^(-1/x + c)
= ce^(-1/x)

so, (B)

Answer 2

1C