true-false quiz chapter 7

the equation y'=x+y is separable

false

all solutions of the differential equation y'=-1-y^4 are decreasing functions

true

consider the differential equation y'=g(y) where g(y) is a differentiable function of y. it is not possible for y to exhibit oscillatory behavior.

true

if y is the solution of the initial-value dy/dt = 2y(1- y/5) y(0)=1 then lim y=5 as t goes to infinite

true

the equation y'= 3y-2x+6xy-1 is separable

true

the function f(x)= (lnx)/x is a solution of the differential equation x^2y'+xy=1

true