For the the ode y" - 4y = 0, (a) verify if y_1 = cosh 2x, y_2 = sinh 2x form a fundamental set of the solutions of y" - 4y = 0: (b) form the general solution of the ode y" - 4y = 0.

(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.

the answer to this is a. a^2 + b^2 = c^2