# Solve the following eigenvalue problem?

Posted 1 year ago
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 I have two ODE and I want to find the general solution, but it contains eigenvalues. I try to solve it by using the DSolve, but could not get the solution. Please, anyone can help me to sort out the problem? It would be appreciated. Eq1 = F'[X] + \[Lambda]^2*F[X] == 0 Eq2 = G''[Y] + (\[Epsilon]*(Y^2 Subscript[A, 1] + Y*Subscript[A, 2] + Subscript[A, 3]))/Subscript[A, 4]*\[Lambda]^2*G[Y] == 0  Attachments:
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Posted 1 year ago
 Suggestions.(1) Place short code questions in the question rather than an attached notebook.(2) Avoid upper case for function and variable names (less likely to get confused for built-in symbols).(3) Keep the code as simple as possible-- avoid Subscript when it is not needed for example.(4) Explain what results you got and why they are not doing what you want.Here are the examples. DSolve[{f'[x] + \[Lambda]^2*f[x] == 0 }, {f[x]}, x] (* Out[2]= {{f[x] -> E^(-x \[Lambda]^2) C[1]}} *) DSolve[{g''[y] + (\[Epsilon]*(y^2 a1 + y*a2 + a3))/ a4*\[Lambda]^2*g[y] == 0 }, {g[y]}, y] (* Out[3]= {{g[y] -> C[1] ParabolicCylinderD[(-4 a1^(3/2) Sqrt[a4] + I a2^2 Sqrt[\[Epsilon]] \[Lambda] - 4 I a1 a3 Sqrt[\[Epsilon]] \[Lambda])/( 8 a1^(3/2) Sqrt[ a4]), ((-1)^(1/4) a2 \[Epsilon]^(1/4) Sqrt[\[Lambda]])/( Sqrt[2] a1^(3/4) a4^(1/4)) + ((-1)^(1/4) Sqrt[2] a1^(1/4) y \[Epsilon]^(1/4) Sqrt[\[Lambda]])/a4^(1/4)] + C[2] ParabolicCylinderD[(-4 a1^(3/2) Sqrt[a4] - I a2^2 Sqrt[\[Epsilon]] \[Lambda] + 4 I a1 a3 Sqrt[\[Epsilon]] \[Lambda])/(8 a1^(3/2) Sqrt[a4]), I (((-1)^(1/4) a2 \[Epsilon]^(1/4) Sqrt[\[Lambda]])/( Sqrt[2] a1^(3/4) a4^(1/4)) + ((-1)^(1/4) Sqrt[2] a1^(1/4) y \[Epsilon]^(1/4) Sqrt[\[Lambda]])/a4^(1/4))]}} *) It is not clear from the post what were the desired results.
Posted 1 year ago
 Thanks for your help. I have noted all your points. Actually, these equations (Eq.1 and 2) they came from PDE. I used separation of variables method and then equate with the Lambda so it becomes eigenvalue problem. The first equation can be solved but the second one is difficult to solve it is a Sturm-Liouville problem. I want to find the eigenvalue (Lambda) and eigenfunction. So how can I solve it? How can I solve the general solution of the equation?PDE: D[\[Theta][x, y], {x, 1}] == Subscript[A, 4]/(\[Epsilon]*(Y^2 Subscript[A, 1] + Y*Subscript[A, 2] + Subscript[ A, 3])) D[\[Theta][x, y], {y, 2}] where A1, A2, A3,\Epsilon are constants.Initial Condition  \[Theta] (0, y) == 0 Boundary Condition \[Theta]' (x, 1) == 0 
Posted 1 year ago
 Please make sure you know the rules: https://wolfr.am/READ-1STThe rules explain how to format your code properly. If you do not format code, it may become corrupted and useless to other members. Please EDIT your post and make sure code blocks start on a new paragraph and look framed and colored like this. int = Integrate[1/(x^3 - 1), x]; Map[Framed, int, Infinity]