Verified answer

Ответ:

Пошаговое объяснение:

y'' - y' - 2y = 0

a² - a - 2 = 0

D = 1 + 8 = 9

a1 = (1-3)/2 = -1

a2 = (1 + 3)/2 = 2

y(x) = C1e⁻ˣ + C2e²ˣ

C1 + C2 = 3

-C1 + 2C2 = 0

3C2 = 3

C2 = 1

C1 = 2

y(x) = e⁻ˣ + 2e²ˣ

5)

y'' - 6y' + 13 = 0

a² - 6a + 13 = 0

D = 36 - 52 = -16

a1 = 4i

a2 = -4i

y(x) = С1 * cos4x + C2 * sin4x

C1 = 3

4C2 = 11

C2 = 2,75

y(x) = 3cos4x + 2,75sin4x