- #1
CraigH
- 222
- 1
What form should the particular solution of a 2nd order linear non homogeneous differential equation take when the right hand side is a constant?
if the differential differential equation has the form
Ay''+By'+Cy = g(x)
where g(x) is a constant
what form should the particular solution take?
I know if g(x) is an exponential the "trial" solution should be A(e^x)
If g(x) is trigonometric it should be A(sin(x))+B(cos(x))
And If it is a polynomial of degree n it should be A(x^n) + B(x^(n-1)) ... +C(x^0)
But what if the differential equation is just Ay''+By'+Cy = D
Should the trial solution be a polynomial of degree 0?
So I would try
y = D
y' = 0
y'' = 0
which would leave me with
CD=D
which is useless
Please Help!
Thanks!
if the differential differential equation has the form
Ay''+By'+Cy = g(x)
where g(x) is a constant
what form should the particular solution take?
I know if g(x) is an exponential the "trial" solution should be A(e^x)
If g(x) is trigonometric it should be A(sin(x))+B(cos(x))
And If it is a polynomial of degree n it should be A(x^n) + B(x^(n-1)) ... +C(x^0)
But what if the differential equation is just Ay''+By'+Cy = D
Should the trial solution be a polynomial of degree 0?
So I would try
y = D
y' = 0
y'' = 0
which would leave me with
CD=D
which is useless
Please Help!
Thanks!