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
9560 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸How do I find the asymptotes of a curve?
The rectangular hyperbola H has parametric equations: x = 4t, y = 4/t where t is not = 0. The points P and Q on this hyperbola have parameters t = 1/4 and t = 2 respectively. The line l passes through the origin O and is perpendicular to the line PQ.
What is the polar form of the equation: x^2+y^2 =xy+1
Two planes have eqns r.(3i – 4j + 2k) = 5 and r = λ (2i + j + 5k) + μ(i – j – 2k), where λ and μ are scalar parameters. Find the acute angle between the planes, giving your answer to the nearest degree.