# Tagged Questions

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### Integral formulation for LDE

I am trying to put the system in a integral formulation. All goes well for the first integration as I obtain What I don't know is how to perform the second integration in this last term. My ...
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### Integral of [(1+2y^2)/(3-y)]dy (obtained from a differential equation)

This question actually arises from this Differential Equations question: Find the family of solutions for: (1+2y^2)(dy/dx) + (3-y)cosx = 0 I ruled out the methods I've so far learned in class ...
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### Second order homogenous non-linear DE: $3(x')^2 - 2x''x=0$

How do I solve this for $x$? $$3\dot{x}^2-2\ddot{x}x=0$$ $$\Leftrightarrow$$ $$3(x')^2 - 2x''x=0$$ Note: This comes from my working here(on stack exchange meta sandbox[newest activity]) List of ...
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### Green's function for $y''+y=f(x)$

This example is taken from the Wikipedia's article. Namely, find the Green's function for $$y'' + y = f(x)$$ with boundary conditions: $$y(0) = y(\frac {\pi} {2}) = 0.$$ The defining equation for ...
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### Two very similar solutions to a differential equation through two different methods

In our differential equation class, we learned of two methods to solve elementary differential equations: integration factors and seperation. We had to solve the differential equation (k is a ...
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### What is the Riemann surface of the exponential integral?

I have recently encountered a differential equation whose solution has a term \frac{1}{2}e^{-\frac{1}{2 \varepsilon} e^{i \tau}} \int_{\tau_0}^\tau e^{\frac{1}{2 \varepsilon} e^{i ...
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### Integrate and derivative

i'm not able to explain the following step: $\frac{1}{k+v(x)}=\frac{d^2 v}{dx^2}$ by integrating this equation: $(C-\frac{1}{k+v(x)})^{\frac{1}{2}}=\frac{dv}{dx}$ Please, if somebody can help i'll ...
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### Integrating $d\psi=(x+y)dx +x_0dy$

I am quite embarrassed to ask this question, as I know i have lost track of the concept here, but Ill nevertheless ask it. I was going through Mathematical methods for physicists, and there was an ...
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### Euler's method for first three approximations?

I have tried variations of the problem for an hour at least and cannot get around to sloving this one. Thank you for input!
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### I need to solve $\dfrac{dx}{dt}= 2x(1-0.0001x)-0.01xy, \dfrac{dy}{dt} = -0.5y+0.0001xy$

I need to solve \begin{align} \frac{dx}{dt} &= 2\,x\,(1-0.0001\,x)-0.01\,x\,y \\ \frac{dy}{dt} &= -0.5\,y+0.0001\,x\,y \end{align} Can anyone tell how do we solve such problems, if ...
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### what can we say about the solution of the equation $y'=-y^2$ just by looking at it. [without finding its solution]

I trying to understand differential equations without finding their solution. This is a simple one, so I can verify the ideas from the solution. All ideas are appreciated, since they will help my ...
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### numerical solution of integral equation

Consider the basic type of integral equation. In particular, a volterra integral equation of the first kind. That is, we have the following integral equation $$\int_a^xf(s)g(s,x)~ds=h(x)$$ where $h$ ...
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### How rigorous is multiplying both sides of an eqaution for the differential of a function?

I have to solve this equation: $$-C_0 f + \frac{1}{2}f^2 +\frac{d^2 f}{d X^2}=A$$ where $C_0$ and $A$ are two real nonzero constant; $f:\mathcal{R}\to \mathcal{R}$ I have seen that the person who ...
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### Integral curves and ODE [closed]

How do I find a first-order differential equation having the given family ofcurves as integral curves to that one: all circles through the points $(1, 1)$ and $(-1,-1)$?
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### Integration and ODE

How do I integrate this? $$y'=1+\frac{y}{x}$$ I just don't know how to start. I think I gotta to try some variable changing, but I don't think I'm gonna so far with this.
Please I am trying to solve this differential equation but I do not seem to get the correct answer. Please help thank you. My equation is; $\frac{dc(x)}{dx} = 1+ b\frac{y(x)-y(x-1)}{y(x-1)}$ where b ...