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I have the following problem

$\frac{c_p q_m}{A}\frac{\partial T(x,t)}{\partial t}+\rho c_p \frac{\partial T(x,t)}{\partial x}-\lambda \frac{\partial^2 T(x,t)}{\partial x^2}=0$

I want to find the eigenvalues and eigenfunctions of the differential operator

DEigensystem[D[u[x], {x, 2}] - D[u[x], x], u[x], {x, 0, 1}, 4]

which works and gives the following result

\begin{bmatrix}{} 0 & \frac{1}{4} \left(-1-36 \pi ^2\right) & \frac{1}{4} \left(-1-16 \pi ^2\right) & \frac{1}{4} \left(-1-4 \pi ^2\right) \\ e^x & e^{x/2} (6 \pi \cos (3 \pi x)-\sin (3 \pi x)) & e^{x/2} (4 \pi \cos (2 \pi x)-\sin (2 \pi x)) & e^{x/2} (2 \pi \cos (\pi x)-\sin (\pi x)) \\ \end{bmatrix}

but this does not work

DEigensystem[D[u[x], {x, 2}] - a D[u[x], x], u[x], {x, 0, 1}, 4]

Why?

I constructed a weird test case

Table[DEigensystem[D[u[x], {x, 2}] - a D[u[x], x], u[x], {x, 0, 1}, 2], {a, 0, 20}]

this does work up to a=8

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  • $\begingroup$ So what is the mathematical form of u? This is needed for us to check the eigensystem. $\endgroup$ – David G. Stork Mar 23 '18 at 15:36
  • $\begingroup$ It's the temperatur. But does it matter? $\endgroup$ – OhmSweetOhm Mar 23 '18 at 15:38
  • $\begingroup$ If it suffices for you to obtain the eigensystem for numeric a then you should have a look at NDEigensystem . $\endgroup$ – Henrik Schumacher Mar 23 '18 at 19:04

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