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
9904 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Prove by induction that 6^n + 4 is divisible by 5 for all integers n >= 1
If a car of mass 1000kg travels up a slope inclined at 5 degrees at a speed of 20 meters per second calculate the power output of the car's engine (assuming a resistive force due to friction of 500N)
The infinite series C and S are defined C = a*cos(x) + a^2*cos(2x) + a^3*cos(3x) + ..., and S = a*sin(x) + a^2*sin(2x) + a^3*sin(3x) + ... where a is a real number and |a| < 1. By considering C+iS, show that S = a*sin(x)/(1 - 2a*cos(x) + a^2), and find C.
Find all square roots of the number 3 + 4i.