Find the complementary function to the second order differential equation d^2y/dx^2 - 5dy/dx + 6x = x^2
Use the auxiliary equation k2-5k+6=0. Solving this gives roots k=2 and k=3, which are real and distinct roots. This means that the complementary function is of the form y=Ae^(k1x)+Be^(k2x), where k1 and k2 are roots of the auxiliary equation and A and B are real constants. Therefore the complementary function for this differential equation is y=Ae2t+Be3t.
SM
Answered by Sam M. • Further Mathematics tutor
2975 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Using mathematical induction, prove that n^3+2n is divisible by 3 for all integers n
The quadratic equation x^2-6x+14=0 has roots alpha and beta. a) Write down the value of alpha+beta and the value of alpha*beta. b) Find a quadratic equation, with integer coefficients which has roots alpha/beta and beta/alpha.
How do I know which substitution to use if I am integrating by substitution?
Write the Maclaurin’s series for f(x)=sin(3x)+e^x up to the third order