Answers>Further Mathematics>A Level>Article

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)e^4x Particular integral: try y_p = ax + b dy_p/dx = a d²y_p/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 y_p = 1/8 x + 1/16 ANSWER: (A+Bx)e^4x + 1/8 x + 1/16

Answered by Oliver F. • Further Mathematics tutor

9781 Views

Find the general solution to the differential equation: d^2y/dx^2 - 8 dy/dx +16y = 2x

Related Further Mathematics A Level answers

A curve has polar equation r = 1 + cos THETA for 0 <= THETA <= 2Pi. Find the area of the region enclosed by the curve

Find the square root of i

Prove by mathematical induction that, for all non-negative integers n, 11^(2n) + 25^n + 22 is divisible by 24

Expand (1+x)^3. Express (1+i)^3 in the form a+bi. Hence, or otherwise, verify that x = 1+i satisfies the equation: x^3+2*x-4i = 0.