Can someone double check everything and provide correct answer for every part
A homogeneous second-order linear differential equation, two functions y, and y2, and a pair of initial conditions are given. First verify that y, and ya are solutions of the differential equation. Then find a particular solution of the form y = c,y, + c2y2 that satisfies the given initial conditions. Primes denote derivatives with respect to x.
L-=(O),Xg=(O)Xx_2X=Xx_=X:0=X+XZ+X
Why is the function y, = e- a solution to the differential equation? Select the correct choice below and fill in the answer box to complete your choice.
and
its second derivative, y,"
are substituted into the equation, the result is a true statement.
, are
substituted into the equation, the result is a true statement.
the answer box to complete your choice.
,are
substituted into the eguation, the result is a true statement.
B.
and its second derivative, Y2" = 1(2-2x+x2)e(-x) are substituted into the equation, the result is a true statement.
The particular solution of the form y = c, Y, + c22 that satisfies the initial conditions y(0) = 6 and y'(0) = -- 1 is = =[6e(-x)+5xe(-x)