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 Apr 18 comment Simplify this trigonometric identity $(1-\cos^2)(1+\cos^2)$ Is this simpler? 1-cos^4 Apr 9 comment Particular solution for non-homogeneous differential equation In Mathematica, you can try DSolve[u''[t] + u'[t]/t - u[t]/t^2 == a Sin[t], u[t], t] which returns a reasonably nice answer. It gives an answer for arbitrary g(t) (instead of a Sin[t]). Feb 12 comment How calculate the rest of the division 2/7 Here's an explanation of the mod operation: en.wikipedia.org/wiki/Modulo_operation Feb 12 answered How calculate the rest of the division 2/7 Oct 24 comment How can I plot curves relative to other curves? Here is one way to warp the space on which a plot is drawn: mathematica.stackexchange.com/a/24974/1783 Jun 20 comment Symbol in Linear Algebra Google is your friend: en.wikipedia.org/wiki/Element_(mathematics) Jun 20 comment Symbol in Linear Algebra It is like a little "e" and means "element of", so "o with a bar" is an element of the set S. But really, you are on the wrong site... this is for users of Mathematica (the software), so your question will probably be closed as off-topic. Jun 3 comment Steps to go from $\frac{\frac{1}{x}-y}{\frac{1}{x}+y}$to $\frac{1-xy}{1+xy}$ Simplify[((1/x) - y)/((1/x) + y)] works Dec 15 awarded Caucus Aug 24 comment How to apply Gaussian kernel to smooth density of points on 2D (algorithmically) For the theory of filtering, look up "convolution" which is the mathematical operation being performed by commands like GaussianFilter. Wikipedia as always is a good reference: en.wikipedia.org/wiki/Convolution Jan 6 comment In search of an angle Do you know the equations or slopes of the green lines? Jan 4 comment Solving: How to find an inverse function for this function? What do you want the inverse to be when x=0? Oct 28 awarded Commentator Sep 19 awarded Editor Jul 17 comment How to calculate the number of factorizations of a square matrix? Have you seen this? cse.unsw.edu.au/~jingling/papers/laa.pdf May 30 comment Reducing an integral equation to a differential one Suppose that there were two functions f_1(x) and f_2(x) both of which have the same answer K(a-b). Take the difference between the integrals of f_1(x) and f_2(x) and this has to be zero. What does that tell you? May 30 comment Reducing an integral equation to a differential one Here's a hint: suppose f(x) was equal to a constant. What would the integral be? May 15 comment Solve $(x^2 + 5)^2 - 15(x^2 + 5) + 54 = 0$ Try this: define a new variable z=x^2+5 and solve z^2-15z+54 using the quadratic formula. Then solve for x in terms of z. May 14 awarded Caucus May 12 comment Fractal Analysis Perhaps the most fundamental way to compare two fractals would be by their dimension.