Tagged Questions

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Eigenvalues of Differential Equation with Boundary Condition

Here is a problem from my homework assignment that I am struggling with: Consider the differential equation $\frac{d^2\phi}{dx^2}+\lambda\phi=0$. Determine the eigenvalues $\lambda$ if $\phi$ ...
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Eigenvalue of Heun's function and its computation

It is known that the Heun's differential equation: \frac{d^2 w}{dz^2} + (\frac{\gamma}{z}+\frac{\delta}{z-1}+\frac{\epsilon}{z-a})\frac{dw}{dz}+\frac{\alpha \beta z -q}{z(z-1)(z-a)} ...
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Find solutions for an differential equation system

I have a differential equation system $x_1'(t) = -x_2(t)$ $x_2'(t) = -x_1(t)$ I see that I can write $\dot{x} = Ax$ where $A = \begin{pmatrix}0 & -1 \\ -1 & 0\end{pmatrix}$ The complete ...
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When I do my homework (stability theory), I must use the knowledge to the matrix. But I don't remember it :(. Here's my problem: For the system of equations: $$\begin{cases} & \text{ } ... 3answers 78 views another generalized eigenvector question I have$$ A = \left( \begin{array}{ccc} -4 & 9 & -4 \\ 0 & 0 & 0 \\ 6 & -13 & 6 \end{array} \right) $$whose eigenvalues are \{0,0,2\}. For \lambda=2, I have ... 1answer 1k views How to sketch the phase portrait near the critical point at the origin. A linear system and its general solution. dx/dt = 6x - 2y dy/dt = 4x + 2y It has a general solution of this:$$\begin{bmatrix} x(t) \\ y(t) \end{bmatrix} = A\begin{bmatrix} cos(2t) \\ ...
Consider the matrix $A=\begin{bmatrix} 1 & 1 \\ -1 & 3 \end{bmatrix}$ I found the eigenvalue $\lambda=2$ with multiplicity $2$. However, the general solution I found degrees with the answer ...
I’m trying to find the eigenvalues and eigenvectors of the Singular Sturm-Liouville operator: $$Lu=xu''+u'$$ $$u(1)=0$$ $$u(0) \text{ is finite}$$ $$0 < x < 1$$ My approach to solving ...