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
9862 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Using de Moivre's theorem demonstrate that "sin6x+sin2x(16(sinx)^4-16(sinx)^2+3)"
Evaluate the following product of two complex numbers: (3+4i)*(2-5i)
What is the meaning of having a 3 by 3 matrix with determinent 0. Both geometrically and algebriaclly.
For what values of x is Cosh^2(x) - Sinh(x) = 5 Give your answer in the form of a logarithm