Particular solution for a non-homogeneous second order linear differential equation : d²y/dx² + 5dy/dx - 6y = 7e^x

Suppose that X1=-1, x2=2, x3=4, x4=-3 is a solution of a non-homogeneous linear system Ax = b and that the solution set of the homogeneous system Ax=0 is given by the formulas: x1= -3r +4s, x2=r-s, x3=r, x3=s a) Find the vector form of the general solution of Ax=b b) Find the vector form of the general solution Ax=b.

Let A be a 3x3 matrix such that At=-A(i.e.,A is a skew - symmetric). Find the general solution of the homogeneous equation Ax=0.