Question

Question 14

Use the method of variation of parameters to find a particular solution using the given fundamental set of solutions {x1,x2}.

x′=(−10−1−1)x+(−25t),  x1=e−t(01),  x2=e−t(−1t)

(Enter the solution as a 2x1 matrix.)

xp(t)=

Question 14 Use the method of variation of parameters to find a particular solution using the given fundamental set of solutions (xi,x2 (Xi, X2l x'=(-1 0 1-1 (Enter the solution as a 2x1 matrix.) Xp (t) =

Answer 1

"X' = (-1 0 -1 -1) x + (- 2 5 t) , x' = Ax + g(t) complementary solution is given y_c (x) = c1 (0 e^-t) + c_2 (- e^-t t e^-t) x = (0 -e^-t e^-t te^-t) Now, we find inverse this matrix cy A = [a b c d] , A^-2 = 1/