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Answer:
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)