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
9751 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸How do you deal with 3 simultaneous equations? (Struggling with Q7 of AQA specimen paper 1)
Given sinhx = 0.5(e^x - e^-x), express its inverse, arcsinhx in terms of x.
solve the 1st order differential equation 2y+(x*dy/dx)=x^3
Use algebra to find the set of values of x for which mod(3x^2 - 19x + 20) < 2x + 2.