For these six numbers, e3, 3e, eπ, πe, 3π, π3, how to arrange them in the increasing order? This problem is taken from the today test: National Higher Education Entrance Examination.

Nov 7, 2021 · Find the general solution to $xy' = 2y + x^3e^x$ Ask Question Asked 4 years, 2 months ago Modified 4 years, 2 months ago

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

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, 9 months ago Modified 9 years, 6 months ago

I'm struggling with a seemingly simple problem in differential equations. If the Wronskian W of f f and g g is 3e4t 3 e 4 t, and if f(t) =e2t f (t) = e 2 t, find g(t) g (t). So from that I made a first order linear …

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). …

Feb 21, 2023 · Evaluate: $\int\frac {3e^ {2x}-2e^x} {e^ {2x}+2e^x-8}dx$ Ask Question Asked 2 years, 10 months ago Modified 1 year, 2 months ago

I need to find the value of $\displaystyle \int _0^ {2\pi}\sin^2 \left (\frac {-\pi} {6}+3e^ {it} \right)dt$. I figured I could use contour integration and the Cauchy-Goursat theorem to do so.

I have to check whether a graph is planar. The given type is $$ e ≤ 3v − 6 .$$ From Wikipedia: Note that these theorems provide necessary conditions for planarity that are not sufficient cond...