The final ordering of the six numbers is therefore 3e <e3 <πe <eπ <π3 <3π 3 e <e 3 <π e <e π <π 3 <3 π. As an aside, we've used a number of the properties of e e and log log during the derivations, so …

Dec 14, 2019 · but I end up cancelling the term C2e2x C 2 e 2 x. What particular solution do we have to propose?

Feb 3, 2016 · I have to evaluate the integral $\int_ {0}^ {\infty}t^3e^ {-3t}dt$ using complex analysis techniques (the laplace transform). Can you check my steps, please? $$\int_ {0}^ {\infty}t^3e^ {-3t}dt …

Sep 9, 2024 · Can p′(x) − 2xp(x) =x3 p (x) 2 x p (x) = x 3? p p would have to be quadratic, leading coefficient −1 2 − 1 2. The linear term would have to be 0 0 (considering when you let x = 0 x = 0). …

Aug 14, 2015 · I tried to use integration by parts to do this and I let u =x3 u = x 3 and dv =exdx d v = e x d x. So I get

Nov 7, 2021 · Find the general solution to xy′ = 2y +x3ex x y = 2 y + x 3 e x Using the equation for the nonhomegenous ODE

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Solve the following If f(x) =e−x + 2e−2x + 3e−3x + ⋯ f (x) = e x + 2 e 2 x + 3 e 3 x + Then find ∫ln 3 ln 2 f(x)dx ∫ ln 2 ln 3 f (x) d x I don't have any idea.

Feb 21, 2023 · Given ∫ 3e2x−2ex e2x+2ex−8dx ∫ 3 e 2 x 2 e x e 2 x + 2 e x 8 d x My attempt- Substitute u =ex ⇒ du = dx.ex u = e x ⇒ d u = d x e x The integral becomes

Apr 8, 2016 · (Laplace Method) y′′ − 4y′ = 6e3t − 3e−t y ″ 4 y ′ = 6 e 3 t 3 e t Ask Question Asked 9 years, 10 months ago Modified 9 years, 6 months ago