Mathematics

Sylvia

4 March, 13:43

Consider the homogeneous second-order linear differential equation y′′+4y′-12y=0. Which of the following pairs gives two solutions to this equation? A. y1=e2x, y2=e-6x B. y1=e3x, y2=e1x C. y1=e2x, y2=e-2x D. y1=e-12x, y2=xe-12x E. y1=cos (-12x), y2=sin (-12x) F. y1=e-4x, y2=e-12x Then for these solutions find a particular solution of the form y=c1y1+c2y2 that satisfies the initial conditions y (0) = -5, y′ (0) = 0. y = y1 + y2.