Find the general solution to the differential equation: d^2y/dx^2 - 8 dy/dx +16y = 2x
d2y/dx2 - 8 dy/dx +16 y = 2x Auxiliary Equation: m2 - 8m +16 = 0 (m - 4)2 = 0 m = 4 (repeated root) Complimentary function: y = (A+Bx)e4x Particular integral: try yp = ax + b dyp/dx = a d2yp/dx2 = 0 0 - 8(a) + 16(ax + b) = 2x -8a + 16ax +16b = 2x Equate x1 terms: 16a = 2 => a = 1/8 Equate x0 terms: -8a + 16b = 0 => b = a/2 = 1/16 yp = 1/8 x + 1/16 ANSWER: (A+Bx)e4x + 1/8 x + 1/16
OF
Answered by Oliver F. • Further Mathematics tutor
9413 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Find the eigenvalues and corresponding eigenvectors of the following matrix: A = [[6, -3], [4, -1]]. Hence represent the matrix in diagonal form.
Can you show me how to solve first order differential equations using the integrating factor method?
How can we solve a limit having an indetermination of the type 0/0 or infinity divided by infinity?
Use de Moivre's theorem to calculate an expression for sin(5x) in terms of sin(x) only.