Характеристическое уравнение
k^2 - 12k + 35 = 0
D = 4
k1 = (12 + 2)/2 = 7
k2 = (12 - 2 )/2 = 5
y = c1*e^(5x) + c2*e^(7x)
y(0) = c1 + c2 = 3
y ' (0) = (c1*e^(5x) + c2*e^(7x) ) ' = 5c1*e^(0) + 7*c2*e^(0) =
= 5c1 + 7c2 = - 4
c1 + c2 = 3
5c1 + 7c2 = - 4
c1 = 12,5
c2 = - 9,5
y = 12,5 *e^(5x) - 9,5 *e^(7x)