# Tagged Questions

Questions on (ordinary) differential equations. For questions specifically concerning partial differential equations, use the (pde) tag.

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### Solution of Homegeneous Differential Equation

"What if the M and N are of with the different degree. Is the solution exist?" If $M(x,y)dx+N(x,y)dy=0$ are homogeneous function and of the same degree. What if the M and N are of with different ...
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### Find the value of $y(1)$ of the ODE $y'+y=|x|$.

Let $y$ be the solution of $$y'+y=|x|$$ for $x\in\mathbb{R}$ and $y(-1)=0$. Then the value of $y(1)$ is $\frac{2}{e}-\frac{2}{e^2}$ $\frac{2}{e}-2e^2$ $2-\frac{2}{e}$ $2-2e$ I don't know what to ...
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### Intuitive explanation of a stochastic PDE

Lindgren et al 2011 connects Gaussian Markov Random Fields (which have fast calculation properties due to the Markov attribute) and Gaussian Processes (which can model many types of data). The ...
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### Modeling - First Order vs Higher Order Differential Equations

Throughout my engineering education, I've only witnessed modeling using First Order differential equations. Almost all of my Higher Order knowledge was given either via a spring or heat equation or ...
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### General solution of a nonlinear differential equation

Nonlinear differential equation gone beyond my field of expertise but I'd like to know the details of a problem and to do that I should know the general solution of the following nonlinear ...
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### How can I solve $y''=\frac{a}{y^2}$ where a is a (positive) constant?

Actually, I found out a way to solve that, but I can't get rid of complex numbers. And it does not make sense when it comes to complex numbers as the original question that involves this differential ...
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I am dumbfounded as to how to solve this particular equation: Given $y(x+h)=y(x)-h(\alpha y(x)+\beta), y(0)=n$, where $\alpha$, $\beta$ and $n$ are constants, find $\lim_{h\to0}y(x)$ I tried solving ...
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### Non homogeneous Second order ODE

How to solve differential equations of the form: $$\ddot{r}+A(t)r=B(t)$$ In particular I would like to solve the following differential equation: $$\ddot{r}-\omega^2r=\frac{V}{t}$$ Where $\omega$ and ...
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### Help in solving the differential equation $y'(x)=y(x) + \int_0^1ydx$

If $y(x)$ satisfies the eqn $$y'(x)=y(x) + \int_0^1ydx$$ Where $$y(0)=1$$ Then what will be the value of $$y(ln\frac{11-3e}{2})$$ I tried differentiataing both sides wrt $x$, I got $$y''(x)= y'(x)$$ ...
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### Solving differential equation of third degree

If differential equation of the curves $$c(y+c)^2 = x^3$$ where 'c' is an arbitary constant is $$12y(y')^2 + ax = bx(y')^3$$ What is the value of a+b? I tried differentiating the curve given and ...
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### Request for Introduction to Complex valued PDE's and their applications in math and physics

On Mathematica.stackexchange there is a recent question concerning PDE's with complex damping coefficients, see http://mathematica.stackexchange.com/questions/119870/can-i-use-operators-of-the-form-...