Thread: systems of linear equations

Let x=x1(t), y=y1(t) and x=x2(t), y=y2(t) be any two solutions of the linear nonhomogenous equation

x'=p11(t)x+p12(t)y+g1(t),
y'=p21(t)x+p22(t)y+g2(t)

Show that x=x1(t)-x2(t), y=y1(t)-y2(t) is a solution of the corresponding homogenous system.

Thank you!

Originally Posted by morganfor

Let x=x1(t), y=y1(t) and x=x2(t), y=y2(t) be any two solutions of the linear nonhomogenous equation

x'=p11(t)x+p12(t)y+g1(t),
y'=p21(t)x+p22(t)y+g2(t)

Show that x=x1(t)-x2(t), y=y1(t)-y2(t) is a solution of the corresponding homogenous system.

Thank you!

Substitute into the equations and show that (x1,y1) and (x2,y2) being solutions implies that (x1-x2,y1-y2) is also a solution.

CB