Use the substitution y equals x Superscript r to find a general solution to the given equation for x greater than 0. x cubed y triple prime (x )plus 3 x squared y double prime (x )minus 9 xy prime (x )minus 24 y (x )equals0

The problem solution  is given in the attachments.

just took the test and my answers down below!

step-by-step explanation:

check the pic :

(a) {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …}

(b) $59 398

step-by-step explanation:

(a) the annual sequence of profits

aₙ = a₁rⁿ⁻¹

the model for the sequence of profits is {a₁, a₁r, a₁r², … a₁rⁿ⁻¹, …} .

(b) profit after 15 yr

  a₁ = $ 30 000

  r = 1.05

a₁₅ = 30 000 × 1.05¹⁴

a₁₅ = 30 000 × 1.979 93

a₁₅ = $59 398

the profit in year 15 will be $59 398.