# Questions tagged [ordinary-differential-equations]

For questions about ordinary differential equations, which are differential equations involving ordinary derivatives of one or more dependent variables with respect to a single independent variable. For questions specifically concerning partial differential equations, use the [tag:pde] instead.

43,441 questions
Filter by
Sorted by
Tagged with
135 views

### How to alter my differential equations to force an abrupt decrease in the solution?

I have the following data sets: ...
1 vote
42 views

### How to obtain $y(1)$ here?

Let $y$ be the solution if $y'+y=|x|,x\in \mathbb{R}$ , and $y(-1)=0$ then $y(1)$ equals (a) $\frac{2}{e}$ (b)$\frac{2}{e^2}$ (c)$2e$ (d) $2e^2$ Actually here $|x|$ is used in the question so I am ...
1 vote
74 views

18 views

36 views

### Need help finding why there no equilibrium solutions to this function

Why does the function $\Bbb dy/\Bbb dx=\sin(x)\cos(y)+\cos(x)$ have no equilibrium solutions? I have already thought of the fact that for $\sin(x)$ to equal 0, $\cos(x)$ would equal 1 and that rules ...
96 views

### Is $f'(x)=f(1/x)$ solvable?

So recently I have been scrolling through Youtube (mainly to find math videos for entertainment, I'll attempt a question on my own every now and then) when I came across this video by Michael Penn ...
26k views

### Can someone intuitively explain what the convolution integral is?

I'm having a hard time understanding how the convolution integral works (for Laplace transforms of two functions multiplied together) and was hoping someone could clear the topic up or link to sources ...
489 views

### Stability of equilibrium of a nonlinear system of ODE's

Suppose we have the nonlinear system of ODE's $$\begin{cases} \dot{x_1} = -\beta x_1 x_2 \\ \dot{x_2} = \beta x_1 x_2 - \gamma x_2 \end{cases}$$ Where we take $\beta, \gamma > 0$ arbitrary for ...
1 vote
57 views

### How is this differential equation simplified? Is $\frac{d(v_a + v_b)}{dt} = \frac{dv_a}{dt} + \frac{dv_b}{dt}$ with $v_a$ and $v_b$ functions of $t$?

How can this equation $$(v_i - v_1)g_1 - C_1\frac{dv_1}{dt}+C_2\frac{d(v_o - v_1)}{dt} = 0$$ be simplified to this? $$v_i g_1 = g_1 v_1 + (C_1 + C_2)\frac{dv_1}{dt} - C_2\frac{dv_o}{dt}$$ I see ...
1 vote
32 views

### General method for finding invariant subsapces of a nonlinear system

Suppose we are given a system: $$\dot{x_{1}} = f_{1}(x_{1},...,x_{n})$$ $$...$$ $$\dot{x_{n}} = f_{n}(x_{1},...,x_{n})$$ And are interested in finding subspaces of the vector space that are invariant ...
71 views

### Solve the Partial Defferential Equation $z+xp-x^2 y q^2-x^3 p q=0$, where $p=\frac{\partial z}{\partial x}$ and $q=\frac{\partial z}{\partial y}$.

I use Charpit Method to solve the problem but calculation is so big. Is there any another method to solve the problem.I think I need some variable transformation which gives me a standard form then I ...
1 vote
14 views

### Eigenvalue problem of an Ordinary Second order Linear Homogeneous differential equation [closed]

Do we have a closed form solution for a canonical form OSLH equation? $$y^{\prime \prime}+(C+x\sin(x))y=0$$ where C is a constant or the eigenvalue. I have checked Andrei D.Polyanin's book "...