I have a following differential equation where w is a function of x alone , a , b c, d,e, k, m, qi's are the constants. How to solve this in mathematica. I used DSolve but I did get any thing in return.

\begin{align*} \frac{d^4w}{dx^4}-2\frac{(2\pi)^2}{b}\frac{d^2w}{dx^2}+\left(\left(\frac{2\pi}{b}\right)^4-a^4\right)w=2\frac{c^4}{d}f(x)\\ f(x)=\frac{1}{km}\sum_1^L P_{i}\sin(n\pi e)\delta(x-q_{i}) \end{align*}

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    $\begingroup$ can you write at least some mma codes? $\endgroup$ – ABCDEMMM Dec 5 '18 at 15:29
  • $\begingroup$ It is unclear whether your summation variable is n or i. Your expression for f[x] does not make a lot of sense the way its written. $\endgroup$ – Bill Watts Dec 6 '18 at 0:34
  • $\begingroup$ The summation is on i $\endgroup$ – acoustics Dec 6 '18 at 7:01

Your differential equation involves DiracDelta. You can, of course, use the Laplace (or Fourier) transform to replace your DE by an algebraic equation. You don't mention the value of $n$ in $sin(n\pi e)$ and, as written, a number of the constants can be ignored or re-scaled.

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