Question

i am finding it challenging to solve D.E of the form y''+by'+(a+d.x^2)y=0

Answer 1

I think you can try looking for an integrating factor first.

Answer 2

i am finding it challenging to solve D.E of the form y''+by'+(a+d.x^2)y=0, where a, b and d are constants

Answer 3

Well since this is second order homogenous DE, I would first try to find the characteristic equation. Since the roots can vary, there will be three cases.

Answer 4

Hmm, is x the independent variable in this equation? I'm just assume that x is constant.

Answer 5

If x is not a constant then the question becomes a second order inhomogeneous DE. You can solve it by undetermined coefficients. The ans would be Y(x) = Y_homo(x) + Y_particular(x)

Answer 6

x is the independent variable. what integrating factor can be used?