# Tagged Questions

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

71 views

### Runge-Kutta methods and butcher tableau

What does the Butcher tableau of a Runge-Kutta method tell me about the method, besides the coefficients in its formulation? In particular, what requirements about it guarantee consistency and ...
54 views

30 views

### Explicit solution to a first order nonlinear ODE

Is there any explicit solution to the following ODE? $G'(z) =aG(z)+bG(z)^α-c$ $G(0) = d_0$
34 views

### Asymptotic behaviour of $\varphi''(x)=F(\varphi(x))$

I'm concerned with the discussion of a ODE, especially the discussion of the solution. I've got the assumptions that there is the relation $\varphi''(x)=F(\varphi(x))$ for all $x$ on $\mathbb{R}$. ...
523 views

55 views

204 views

36 views

### How t find z (unknown) in Runge-Kutta question

I'm trying to solve the below question solve $\dfrac{dx}{dy}=\dfrac{1}{x+y}$ for $x=0.5$ to $z$ using R-K (order $4$) with $x_0=0$, $y_0=1$ (take $h=0.5$). Please help me and tell me how to ...
54 views

### Blow up solution of a Riccati's equation.

Consider the Cauchy problem $$\left\{ \begin{array}{l} \dot x=x(t)^2+t\\ x(0)=0 \end{array} \right.$$ Show that its solution is not defined in $[0,3]$.
42 views

61 views

### Discretization of an Euler-Bernoulli

Given the following Euler-Bernoulli equation: $$(s(x) w(x)'')''= q(x),\ \ x \in [0,1]$$ Could someone explain why the following discretization scheme may not be a good idea? \begin{align*} (sw'')''...
73 views

### Matrix exponent form

We have an equation of matrix exponent $Ae^{Ax}R-e^{Ax}R (P_1 +P_2 x) = Y \tag1$ Given condition $A,R,P_1,P_2,Y$ are constant $3 \times 3$ matrices. R is invertible,orthonormal,determinent ...
98 views

### Second order, inhomogeneous, linear differential equation

I come across this equation in book $$F(z)=(1-\lambda + \mu )f(z) + (\lambda - \mu) zf'(z) + \lambda\mu z^2f''(z)$$ where $\lambda \not= 0$ and $\mu \not= 0.$ My question is how to find $f$? Can ...
67 views

### Converting a series to a recursive expression

Let $e_i$ be a unit vector with one 1 in the $i$-th element. Is the following expression has a recursive presentation? $$y = \sum_{k=0}^{\infty} {\frac{{{X^k} e_i}}{\|{{{X^k} e_i}\|}_2}}$$ where $X$...
114 views

### Uniform perturbative solutions to the Mathieu equation

The Mathieu equation is a second-order linear differential equation given by $$y''(t) + [a - 2q\cos(2t)]y(t) = 0$$ There are two special functions defined as linearly independent solutions to Mathieu'...
30 views

### Saari's homographic conjecture and the actual definition of homography

By the wikipedia definitions found here and here, and especially by the definition implicit in this MSE post, it seems two images are homographic if they are renderings of the same set of points in ...
32 views

### Help solving particular D.E

I'm going through past exams for revision and couldn't get the same answer as the markscheme for this problem. QP http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/...
53 views

### Equation of a curve with a local minimum fixed at $x=a$ when we rotate the curve about the origin.

We have a strangely curved plank. If we place a round weighted object on it, it will rest itself at one point of it, when we incline the plank slowly, the object will gradually move towards a resting ...