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3h
comment Solve $(2x - 1)y'' - 4xy' + 4y = 0$
Even two typos: $P(x)=-2x-\log(2x-1)$, and then do not forget you need $-P(x)$ in the integral. Then everything works out.
4h
comment Solve $(2x - 1)y'' - 4xy' + 4y = 0$
Without carefully looking it seems to be somewhere a simple sign is missing. Look at my integral below, it is quite close to what you've written.
4h
comment Best Approximate Solution of Heat Equation (Diffusive Logistic Equation)
Yes, this is a nonlinear equation, and there is no formula that solves it. The exercise probably asks you to show that your solution will be always between 0 and 1 (note that 0 and 1) solve it
4h
comment Solve $(2x - 1)y'' - 4xy' + 4y = 0$
This may be true, but it is still excessive, there is no need to memorize this kind of formulas.
4h
answered Solve $(2x - 1)y'' - 4xy' + 4y = 0$
5h
comment Solve $(2x - 1)y'' - 4xy' + 4y = 0$
And the first formula is also suspicious. Much better: you know that $x$ is a solution. Make a substitution $y=xv$, where $v$ is a know unknown function. You will end up with a simple separable equation.
5h
comment Solve $(2x - 1)y'' - 4xy' + 4y = 0$
Why do you think that $x e^{2x}$ solves the equation?
5h
comment Best Approximate Solution of Heat Equation (Diffusive Logistic Equation)
Wov, you solved the Fisher's equation using the Duhamel's principle? :)
5h
answered Determining the stability of a system using Lyapunov function
6h
answered Lyapunov Exponent sensitivity to initial conditions
13h
comment Analytical solution of parabolic equation
Change the coordinates $(t,x)\to(t,\xi)$, where $\xi=x-Vt$.
1d
comment Compare analytic model with numerical, mass spring system.
@Danny, I still can answer your questions here if you any.
2d
comment What is the largest t-interval on which guarantees a unique solution?
So, what is the conclusion? Note that your initial condition is given at $\pi$.
2d
comment What is the largest t-interval on which guarantees a unique solution?
No, this is not correct. Start looking at the domain of $\tan$
2d
answered Online course for numerical methods/analysis of PDEs
2d
comment What is the largest t-interval on which guarantees a unique solution?
@KX What about $\tan$?
2d
comment Compare analytic model with numerical, mass spring system.
@Danny, then I would advise you to have some rest and rethink this problem afterwards taking into account all the points I made. Good luck.
2d
comment Compare analytic model with numerical, mass spring system.
Compare from the other end, for n=1,2,3
2d
comment Compare analytic model with numerical, mass spring system.
Here is one more hint: Compare the eigenvalues of $-A$ and $\pi^2n^2/(N+1)^2,\,n=1,2,\ldots$
2d
comment Is this partial differential equation solvable?
What are $r$ and $z$, are these just Cartesian coordinates?