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 Nov2 awarded Revival Jun8 awarded Constituent Jun8 awarded Caucus Nov30 awarded Yearling Jul20 comment Linear ODE, roots of characteristic equation having multiplicity $>1$ @kuch nahi: Sorry, I don't recall ever seeing any specific name for this procedure. Jul19 answered Linear ODE, roots of characteristic equation having multiplicity $>1$ May29 awarded Enthusiast May27 comment How does one compute $\cos((\pi/4)(k-1 ))$? It's probably worthwhile pointing out that we're assuming that $k$ is an integer. This wasn't stated in the original post, but it isn't a very meaningful question otherwise. May19 comment How can I solve this non-linear differential equation? See Hans's comment above. There's no need for complex valued integration constants here as long as you don't ignore the absolute value. May10 comment Confusion about proof in Spivak? @Mark: yes, this fact, which follows directly from the definition of the least upper bound is mentioned in Spivak's proof of the Intermediate Value Theorem (Theorem 7-1 in the 3rd Edition). Apr27 revised Proof that this limit equals $e^a$ fixed a typo Apr27 suggested approved edit on Proof that this limit equals $e^a$ Apr21 comment ODE introduction textbook To save someone else from having to click on the link, the ODE text refer to here is the Edwards & Penney text. Apr21 comment Does this ODE question have closed form solution? Variation of parameters can help solve the inhomogeneous equation, but you need the solutions to the homogeneous equation first. Apr21 comment Does this ODE question have closed form solution? Because of the $e^{A+Bx}$ coefficient, I would be surprised if there was a closed form solution. An approximate solution generated by power series would at least give you an idea about the general behavior of the solution. If you have some particular application in mind, perhaps more information about the parameters (their magnitudes, e.g.) can be used to simplify further? Apr20 comment Prove $\sin(\pi/2)=1$ using Taylor series An outline of this approach can also found in Spivak's Calculus. Mar30 comment How can I find $\int(\sin ^4 x ) dx$? Note that the reduction formulas are typically not something one would note unless you've already seen them, in which case you probably have seen and know how to approach problems like the one posted. The double-angle identities, on the other hand, are certainly helpful for this particular integral. Mar24 answered Prove that $f(x)=e^x$ is Riemann integrable using Riemann sums Mar17 answered Question about the integral of $1/(1+9x^2)$ Mar16 awarded Critic