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
9771 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸It is given that z = 3i(7-i)(i+1). Show that z can be written in the form 24i - k. State the integer k.
Prove by induction that f(n) = 2^(k + 2) + 3^(3k + 1) is divisible by 7 for all positive n.
How do I find the square root of a complex number?
By use of matrices uniquely solve the following system of equations, justifying each step of the calculation: 3x-7y=6, 5y-2x=-3.