Prove the superposition principle for nonhomogeneous equations. Suppose that y1 is a solution to Ly1 = f(x) and y2 is a solution to Ly2 = g(x) (same linear operator L). Show that y = y1 + y2 solves Ly = f(x) + g(x). Differential Equation.

Step-by-step explanation:

Given Data

Suppose That is a solution of L = F(x)

and is a solution  of = g(x)

L is liner operator

∴ = L +

L(y) = F(x) + g(x)

is the solution to  L(y) = F(x) + g(x)

E.g the liner operator be L =

 = f(x)

= g(x)

= + = f(x) + g(x)

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above