- #1
physicsjock
- 89
- 0
hey,
i have this 4th order ode question that I've been working on,
the homogeneous solution was easy enough by finding the particular solution has become a bit annoying,
the ode is
y'''' - 4y'' = 5x2 - e2x
I have gotten the particular solution using variation of parameters, but I used mathematica to do the work, like finding the inverse of the wronskian matrix and integrating the ugly results.
the particular solution i get with mathematica is
yp=1/192 (-30 - 3 E^(2 x) (-5 + 4 x) - 20 x^2 (3 + x^2))
I have checked that this is the particular solution by substitution into the ode and it gives required result.
My question is,
there is no way I was supposed to do this using mathematica, is there a way to approximate the particular solution, like with 2nd order odes?
I tried that in this case,
my particular solution I tried was
(A + Bx + Cx2)+De2x
which is just the sum of the particular solution of x^2 and e^(2x)
Is there some way to estimate the particular solution without using variation of parameters in this question?
i have this 4th order ode question that I've been working on,
the homogeneous solution was easy enough by finding the particular solution has become a bit annoying,
the ode is
y'''' - 4y'' = 5x2 - e2x
I have gotten the particular solution using variation of parameters, but I used mathematica to do the work, like finding the inverse of the wronskian matrix and integrating the ugly results.
the particular solution i get with mathematica is
yp=1/192 (-30 - 3 E^(2 x) (-5 + 4 x) - 20 x^2 (3 + x^2))
I have checked that this is the particular solution by substitution into the ode and it gives required result.
My question is,
there is no way I was supposed to do this using mathematica, is there a way to approximate the particular solution, like with 2nd order odes?
I tried that in this case,
my particular solution I tried was
(A + Bx + Cx2)+De2x
which is just the sum of the particular solution of x^2 and e^(2x)
Is there some way to estimate the particular solution without using variation of parameters in this question?