Find the solution the the differential equation d^2y/dx^2 + (3/2)dy/dx + y = 22e^(-4x)
We first find the complementary function by guessing y=e^(kx). Substituting this into the equation d^2y/dx^2 + (3/2)dy/dx + y = 0. we find k^2 + (3/2)k + 1 = 0 which factorises into (k+2)(k+1/2). So our complementary function is y= Ae^(-2x) + Be^(-x/2). Now we find any particular integral by guessing y = Le^(-4x). Substituting this in to the equation d^2y/dx^2 + (3/2)dy/dx + y = 22e^(-4x) we find that L(16e^(-4x) - 4e^(-4x) + e^(-4x)) = 22e^(-4x) and L=2. So the solution to the differential equation is y= Ae^(-2x) + Be^(-x/2) + 2e^(-4x) //
NE
Answered by Nathan E. • Further Mathematics tutor
7752 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Show, using de Moivre's theorem, that sin 5x = 16 sin^(5) x - 20 sin^(3) x + 5 sin x
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.
Prove by mathematical induction that 11^n-6 is divisible by 5 for all natural numbers n
Prove, by induction, that 4^(n+1) + 5^(2n-1) is always divisible by 21