Question

Section 1.1 Direction Fields: Problem 4 Previous Problem Problem List Next Problem (1 point) A function y(t) satisfies the differential equation dy (a) What are the constant solutions of this equation? Separate your answers by commas (b) For what values of y is y strictly increasing? and liy< Note: You can earn partial credit on this problem. Preview My Answers Suhmit Answers

Answer 1

a )

here

dy/dt = 0

given

dy/dt = - y⁴ - 2 y³ + 15 y² = 0

= (- y²)( y² + 2y - 15 ) = 0

= (- y²) ( y² - 5y + 3y - 15 ) = 0

= (- y²) [ y ( y - 5 ) + 3 ( y - 5 ) ] = 0

= (- y²) ( y - 5 ) ( y + 3 )= 0

= (- y²) ( y - 5 ) ( y + 3 ) = 0

y = 0 , 0 , 5 , -3

b )

y increases between

- 3 < y < 5