# partial differential equation of order 6

is it possible to solve a partial differential equation of order 6 with Mathematica? I tried "DSolve[eq,u,{s,t}]" but the output is just the same as the input. I also tried to add the boundary- and initial-conditions but it doesn't help. May you help me?

To specify my issue, i have to solve the following equation:

eq = -1.3248*^9 - 0.224*(-1.224*Derivative[0, 4][u][s, t] - 1.3248000000000002*^7*Derivative[2, 2][u][s, t]) + 0.224*Derivative[2, 4][u][s, t] + 8.28*^10*(-0.00016*(-1.224*Derivative[0, 2][u][s, t] - 1.3248000000000002*^7*Derivative[2, 0][u][s, t]) - 0.00016*(-1.224*Derivative[2, 2][u][s, t] - 1.3248000000000002*^7*Derivative[4, 0][u][s, t])) - 8.28*^10*(0.00016*Derivative[2, 2][u][s, t] + 0.00016*Derivative[4, 2][u][s, t]) - 8.28*^10*(-0.224*Derivative[2, 2][u][s, t] - 0.00016*(-0.224*Derivative[2, 2][u][s, t] + 8.28*^10*(0.00016*Derivative[2, 0][u][s, t] + 0.00016*Derivative[4, 0][u][s, t])) + 8.28*^10*(0.00016*Derivative[2, 0][u][s, t] + 0.00016*Derivative[4, 0][u][s, t]) - 0.224*Derivative[4, 2][u][s, t] + 8.28*^10*(0.00016*Derivative[4, 0][u][s, t] + 0.00016*Derivative[6, 0][u][s, t])) == 0


and

DSolve[{eq}, u, {s, t}]


just gives me the input back. Even adding boundary conditions doesn't lead to a solution.

What do I do wrong?

I hope you can help me! :)

• I don't think that this will work. First, you should us NDSolve to obtain numerical solutions. I'd say that one cannot hope for symbolic solutions. Second, you might have to specify a domain along with boundary conditions for the PDE. 3.) I doubt that Mathematica's FEM tools can handle PDEs of sixth order directly (Mathematica uses only $C^0$ elements while $C^2$ elements would be necessary.) But maybe you can reformulate your PDE as a coupled sytem of PDE of second order? – Henrik Schumacher Apr 19 '18 at 15:22
• Those coefficients make me sick, literally. This is not supposed to be solve by anything numerical. – Vsevolod A. Apr 19 '18 at 19:03