Question

solve(D^3-5D^2+8D-4)y=e2x​

Answer 1

Answer:

For the equation ( D^3 -5D^2 +8D -4)y = e^2x ,the characteristic equation is

m^3 -5m^2 +8m -4 = ( m-1)( m-2)^2 =0 , roots 1 , 2 ,2 .The complementary

function is yh = C1e^x + C2e^2x + C3xe^2x .

For the particular integral is appropriate the function yp = A(x^2)e^2x.

substituting in the equation gives A = 1/2 .Therefore the required solution is

y = C1e^x + C2e^2x + C3xe^2x +(1/2)(x^2)e^2x .