# Differential Equation: dv/dx Solution

• nishant
In summary, the conversation discusses a differential equation involving dv/dx, k, v, x, R, and C. The conversation includes a question about the exponential integral (Ei) and the request for reasonable values to plot the equation. The conversation ends with a discussion about the use of arbitrary values and the origin of the equation.
nishant

It doesn't look good.I'll let you know why

$$-\frac {1}{2xk}v^2 e^{\frac {x}{vRC}}-\frac {1}{2RCk}v e^{\frac {x}{vRC}}-\allowbreak \frac {1}{2}\frac {x}{R^2C^2k}\mbox{Ei}\left( 1,-\frac{x}{vRC}\right) +v=C$$

Daniel.

sorry but what is Ei?

Exponential integral,http://mathworld.wolfram.com/ExponentialIntegral.html,what else.

Daniel.

Last edited by a moderator:
Nishant, would you kindly supply some reasonable values for k, R, C, and a reasonable initial condition so I could plot it to see what it looks like.

Thanks,
Salty

Edit: I mean numerically (via Runge-Kutta). I dont' think I could plot it using the implicit solution.

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K,R,C are constants

He knew that,he was asking for numbers.

Daniel.

You know Nishant, I shouldn't give you the impression that I "need" reasonable values to plot it. Really, I can just pull them right out of thin air to get a plot: Wait . . . .1,1,1, and another one. See, got a plot. Really though, might be interesting to study how the solution varies as the constants change unless you have a particular set up in mind.

Edit: Here it is, see, 1, 1, 1 and . . . well, you know.

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I am not able to understand Ei,how do u write it in mathematical form?

Well,how did u run into that equation in the first place...?

Daniel.

## 1. What is a differential equation?

A differential equation is an equation that contains one or more derivatives of an unknown function. These equations are used to model various physical, chemical, and economic systems in science and engineering.

## 2. What is the purpose of solving a differential equation?

The purpose of solving a differential equation is to find the exact function or set of functions that satisfy the equation. These solutions can then be used to make predictions and understand the behavior of the system being modeled.

## 3. How do you solve a differential equation?

There are various methods for solving differential equations, depending on the type and complexity of the equation. Some common techniques include separation of variables, substitution, and using fundamental solutions.

## 4. What is the dv/dx solution of a differential equation?

The dv/dx solution is a specific type of solution that is obtained by isolating the dependent variable (often denoted as y) and its derivative (dy/dx) on one side of the equation, and all other terms on the other side. This form of solution is useful for finding the general solution of a first-order differential equation.

## 5. Can you provide an example of solving a differential equation using the dv/dx solution method?

One example of solving a differential equation using the dv/dx solution method is finding the general solution of the equation dy/dx = 2x + 3. By isolating the dependent variable and its derivative, we get dy = (2x + 3)dx. Integrating both sides, we get y = x^2 + 3x + C, where C is the constant of integration. This is the general solution of the given differential equation.

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