I have a conflicting commitment in the Math Department. However, I should be able to be in class a few minutes early if you have questions.

See you in a bit,

Prof. Reitz

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"...how it differs from the rocks"

I have a conflicting commitment in the Math Department. However, I should be able to be in class a few minutes early if you have questions.

See you in a bit,

Prof. Reitz

- Solving $y''(x)-2xy'(x)+y(x) = 0$ using power seriesI'm solving $y''(x) -2xy'(x) +y(x) = 0$ using the power series ansatz $y(x) = \sum_{n=0}^{\infty}a_n x^n$ . Plugging in I get: \begin{equation} \bigg(\sum_{n=0}^{\infty}n(n-1)a_nx^{n-2}\bigg)-2x\bigg(\sum_{n=0}^{\infty}na_nx^{n-1}\bigg)+\sum_{n=0}^{\infty}a_n x^n = 0 \end{equation} \begin{equation} \sum_{n=0}^{\infty}x^n \big((n+2)(n+1)a_{n+2} -2na_n+a_n\big) = 0 \end{equation} \begin{equation} (n+2)(n+1)a_{n+2} -2na_n+a_n = 0 \end{equation} \begin{equation} a_{n+2} = \frac{2n-1}{(n+2)(n+1)}a_n \end{equation} Now we set $a_0$ and $a_1$ as parameters, to observe […]
- Use method of undetermined coefficients to solve $y’’+4y=\sin^3(x)$I solved for the homogenous solution and got $C_1\cos(2x)+C_2\sin(2x)$ but I don’t even know where to start for the particular solution. I tried guessing $A\sin^3(x)+B\cos^3(x)$ but this didn’t work. Any help at all would be appreciated.
- How to solve this ODE $y'^2+(y^2)'/x=1$ in a better way?Strived to solve this ODE, but it seems not be able to work out the the integral after variable substitution. $$\left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^2+2\frac{y}{x}\frac{\mathrm{d}y}{\mathrm{d}x}=1$$ Let $p=\frac{\mathrm{d}y}{\mathrm{d}x}$, we get $$ p+\frac{y}{x}=\pm\sqrt{1+\left(\frac{y}{x}\right)^2} $$ Then substitute $y=vx\implies p=y'=v+xv'$ to arive at $$ 2v+x\frac{\mathrm{d}v}{\mathrm{d}x}=\pm\sqrt{1+v^2}\implies\frac{\mathrm{d}v}{-2v\pm\sqrt{1+v^2}}=\frac{\mathrm{d}x}{x} $$ where the left integral is far from easy to solve. So probably some one has fancier way […]
- Initial conditions for coupled 2nd order ODE, numerical in PythonI have the following problem. I would like to solve the following DGL system numerically in python: $$ \begin{align*} &g'' + \frac{2}{r} g' - \frac{2}{r^2} g - \frac{3}{r} e g^2 - e^2 g^3 - \frac{e}{2r} f^2 - \frac{e^2}{4} f^2g = 0 \ &f'' + \frac{2}{r} f' - \frac{2}{r^2} f - \frac{2e}{r} fg - \frac{e^2}{2} fg^2 […]
- Title: Dynamics of Theta and X with Respect to Alpha of t: Transfer Function Analysis and Final Value Stabilization [closed]$$\frac{d^2\theta}{dt^2}=-Asin(\alpha(t)) \\ \frac{d^2x}{dt^2} = Bsin(\alpha(t)+\theta)$$please find the transfer function of $\theta$ and $x$ with respect to $\alpha$, and provide an appropriate $\alpha$ such that the final values of $\theta$ and $x$ are both $0$. Where $\theta$ and $x$ have initial values $\theta_0$ and $0$ respectively, and A, B are fixed values.
- Diferencial equation non linear: $2y"-2y'+y= e^t\sqrt{y}$I'm not sure if it can be solved using the substitution $u'=y$:$2y"-2y'+y= e^t\sqrt{y}$. My problem is in the part of $e^t\sqrt{y}$.
- Solving second-order nonlinear ODE $x^3y''=(y-xy')^2$ [closed]Given second-order nonlinear differential equation: $x^3\cdot y''=(y-xy')^2$ I have no idea how to solve it. Give me a hint!
- how do you find mean and variance of the simple birth process using the difference differential equation [closed]applied stochastic processses question
- Doubt about guess validation for 2nd order non-homogeneous ODEI am reading a section of a paper (Werning, 2012) where the author proves that the solution of a particular ODE takes a specific form. Extract from the paper (with minor edits) Consider a 2nd order non-homogeneous ODE of the form: \begin{equation} \alpha_1 \mu(t) + \alpha_2 \dot{\mu}(t) + \ddot{\mu}(t) = a(t) \end{equation} with initial conditions […]
- Definite integral in solution of 2nd order non homogeneous ODEProblem I need to solve this second order linear non homogeneous ODE: \begin{align} 0 &= \ddot{x}_{t} - \delta \dot{x}_{t} - \kappa x_{t} + i_t - y_t \nonumber \end{align} where $\delta$ and $\kappa$ are constants, and $x$, $i$, $y$ are variables that depend on time. The following initial conditions are given: $x_{t_1} = \dot{x}_{t_1} = 0$. […]

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