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 Apr 6 answered Series solution to this differential equation Apr 6 comment Series solution to this differential equation Expand $e^{x^2}$ out using its power series (about zero). Then you can multiply out the first few terms of that series with the first few terms of the series its multiplying, and do the "usual" things from there to obtain the recurrence relation for the $a_n$... Apr 5 comment Proving Exponential Convergence Do you know Lyapunov's Theorem/Method for stability? Mar 9 awarded integration Dec 13 awarded Yearling Nov 28 answered Linear Algebra: parametric line in 3d Nov 26 answered Find $\int_0^{y^2}e^{-xy}dx$ using the Leibnitz integral Nov 26 comment Find $\int_0^{y^2}e^{-xy}dx$ using the Leibnitz integral The Leibniz integral rule is for differentiating an integral with respect to a variable that appears both in the limits of integration and the integrand. This is not the situation you have. Nov 26 comment Can you solve $y'+x+e^y=0$ by series expansion? $e^x$? yes. $e^y$? no. Nov 26 revised Volume of sphere - order of integration added 202 characters in body Nov 26 answered Volume of sphere - order of integration Sep 15 awarded Revival May 26 comment Fourier series coefficients proof @Mark yes, every term in the series integrates out to be zero except for the one term where the summation index equals the (fixed) value of $m$, and in that case that term integrates to be $\pi/2$. May 16 comment Intuition behind uniformly continuous functions PS This might be helpful: youtube.com/watch?v=hXkQqCBLRp8 May 16 answered Intuition behind uniformly continuous functions May 12 comment Linear Ordinary Differential Equation with Nonconstant Coefficients Look for a power series solution... Apr 10 comment Understanding the definition of a set with $C^k$ boundary and of the outward pointing normal vector field How would you define the normal vector at the corners of the square? Think about what it means to be the normal vector there... And why a lack of $C^1$ is a problem... Apr 10 comment Understanding the definition of a set with $C^k$ boundary and of the outward pointing normal vector field How about $U$ the interior of a square? Then the boundary of $U$ is continuous, but not smooth ($C^1$) at the corners. Apr 8 awarded Enlightened Apr 8 awarded Nice Answer