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Questions on symbolically or numerically determining the eigenvalues of matrices (Eigenvalues, Eigensystem) or differential equations (DEigenvalues, DEigensystem, NDEigenvalues, NDEigensystem) in Mathematica. Also includes determining the eigenvalues of differential equations with DSolve or NDSolve.

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Using ParametricNDSolve does not work for certain parameters

I want to solve the following second-order DE $$ \ddot{w}(t) H(w(t))+\frac{1}{2}(\dot{w}(t))^2 H'(w(t))+g(w(t))(c_0 (\overline t-\underline t)-w(t)) =0, $$ with boundary conditions $\dot{w}(\overline …