1
vote
1answer
39 views

Constrained Newton-Raphson method

Peace be upon you, I want to solve a system of two equations in which the existence of $ln\left(\frac{\alpha}{\alpha+\beta}\right)$ function makes some limitations in iterations of the Newton-Raphson ...
2
votes
4answers
67 views

How to solve this kind of equation $(x^y=y^x)$

I'm little bit stuck with this system of equations : $x^y=y^x$ and $x^3=y^2$ An obvious solution is $(x,y) = (1,1)$ but what about the solution $(9/4,27/8)$ ? I know the relation $a^r=e^{r ...
1
vote
1answer
37 views

Solution of $d^2u/dx^2 + u/A = 0 \ (\text{or } \ C),$ with conditions

Does the following ODE: $$d^2u/dx^2 + u/A = 0 \quad (\text{or } \ C),$$ have a solution with the conditions: $$ \left.\frac{d^2u}{dx^2}\right|_{x=0} = 0, $$ $$u(x=0) = B$$ and $$ ...
1
vote
1answer
40 views

Can the variables of $y = A + B \mathrm{e}^{C t}$ be solved analytically given 3 sets of points?

Given the non-linear equation $y = A + B \mathrm{e}^{C t}$ and 3 sets of points: ($y_1$, $t_1$), ($y_2$, $t_2$), ($y_3$, $t_3$), can the variables $A$, $B$, and $C$ be calculated analytically? ...
0
votes
1answer
73 views

When does this non linear 2 equation system have solutions? What is the solution?

I need to solve the following system: $$ \begin{cases} a x_0^2 = \exp{ \left( -\dfrac{x_0^2}{4 \sigma^2} \right) } +a r^2 \\ \exp{ \left( -\dfrac{x_0^2}{4 \sigma^2} \right) } + 4 a \sigma^2 = 0 ...
0
votes
1answer
54 views

How to solve this system of ODE's?

I'm not sure how to proceed to solve this system of ODE's; $$ \begin{bmatrix}\dot{x}_1 \\\dot{x}_2\end{bmatrix}=\begin{bmatrix} \cos t & -\sin t\\ \sin t & \cos t ...
0
votes
1answer
62 views

Creating an exponential scale

Good morning, I am trying to create an exponential scale for attributing values in a scoring model. Here is the function I was thinking of using: y = z^x Where: y = Score X = Risk assessment ...
0
votes
2answers
57 views

Linear system of ODEs

Given is the ODE system $y'=\left(\begin{matrix}1\\1\\0\\ \end{matrix}\right)+\left(\begin{matrix}0&0&0\\0&k&0\\0&-k&k\\ \end{matrix} \right)y$ with boundary conditions ...
0
votes
3answers
125 views

Solve these systems of equations

Consider the two equations below: $$ y_{1}=\left(1-\frac{a_{1}}{x}\right)e^{-\dfrac{\alpha\, a_{1}}{x}}\\ y_{2}=\left(1-\frac{a_{2}}{x}\right)e^{-\dfrac{\alpha\, a_{2}}{x}} $$ Given $y_{1}$, ...
0
votes
1answer
45 views

How to best solve a system of equations like this one

I need some help trying to solve a system of two equations with two unknowns. Background: This is not homework, just hobby. I have some LEDs that I needed to identify, but the manufacturer datasheet ...