Afunction y(t) satisfies the differential equation dy dt = y4 − 9y3 + 20y2. (a) what are the constant solutions of the equation? (b) for what values of y is y increasing? (c) for what values of y is y decreasing?

a) y = 0, y = 4 and y = 5

b) y ⊂ (- ∞, 0) ∪ (0, 4) ∪ (5, ∞)

c) y ⊂ (4,5)

Step-by-step explanation:

Data provided in the question:

function y(t) satisfies the differential equation:

= y⁴ − 9y³ + 20y²

Now,

a) For constant solution

= 0

or

y⁴ − 9y³ + 20y² = 0

or

y² (y² - 9y + 20 ) = 0

or

y²(y² -4y - 5y + 20) = 0

or

y²( y(y - 4) -5(y - 4)) = 0

or

y²(y - 4)(y - 5) = 0

therefore, solutions are

y = 0, y = 4 and y = 5

b) for   y increasing

> 0

or

y²(y - 4)(y - 5) > 0

or

y²

y ⊂ (- ∞, 0) ∪ (0, 4) ∪ (5, ∞)

c) for   y decreasing

< 0

or

y²(y - 4)(y - 5) > 0

or

y²

y ⊂ (4,5)

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

bull

step-by-step explanation: