let $$y''+p(t)y'+q(t)y=g(t)$$ then By the Abel theorem wronskian equals to : $$W= c e^{\int p(t)dt}$$ Now We want to generalise this to a 3...
Published: Aug 21, 2026
So I've been playing around with my calculator. In degrees mode with my casio calculator, I typed, "$\arctan(1)$" and got an answer of 45. In radian ...
Published: Aug 21, 2026
I need to graph a rectangle on the Cartesian coordinate system. Is there an equation for a rectangle? I can't find it anywhere.
Published: Aug 21, 2026
For example let's say I wanted to prove that: $$\lim_{x \to \infty} \frac{1}{x} = 0$$ Normally I would use epsilon-delta for such proofs but then I s...
Published: Aug 21, 2026
$$\begin{align} \int \sec x \, dx &= \int \cos x \left( \frac{1}{\cos^2x} \right) \, dx \\ &= \int \cos x \left( \frac{1}{1-\sin^2x} \right) \, dx...
Published: Aug 21, 2026
Find a regular equilateral and equiangular 16-sided polygon that has vertices that are lattice points. What is the minimum side length? Find the vertices ...
Published: Aug 21, 2026
Given that $G$ is the centroid of $\Delta ABC$, $GA = 2\sqrt{3}$ , $GB = 2\sqrt{2}$, $GC = 2$ . Find $[\Delta ABC]$. What I Tried: Here is a picture :- I ...
Published: Aug 21, 2026
This is my second attempt to solve exercise 1.6H from Vakil: Assume $F$ is a covariant right-exact functor and show that we get a map $HF^i \rightarrow H^...
Published: Aug 21, 2026
I was writing a C++ class for working with 3D vectors. I have written operations in the Cartesian coordinates easily, but I'm stuck and very confused...
Published: Aug 21, 2026
For a function $f(x)$, it is possible to write it as a taylor series centered around a point $x=a$: $$f(x)=\sum_{n=0}^{\infty}\frac{f^{(n)}(a){(x-a)}^{n}}...
Published: Aug 21, 2026