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.

If you simplify by factoring out $e^ {2t}$ and cancelling, that would give you $$g' - 2g = 3e^ {2t},$$ instead of $g'-2g = 3e^ {4t}$, which is what you had. So it looks like you made a simplification error.

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

Sep 9, 2024 · Solving $\int_0^ {\infty}x^3e^ {-x^2}dx$ [duplicate] Ask Question Asked 1 year, 3 months ago Modified 1 year, 3 months ago

Apr 8, 2016 · Taking the Laplace Transform to both sides of the ODE we get \begin {align*} s^2Y (s)-s (1)- (-1)-4 [sY (s)-1]&=\frac 6 {s-3}-\frac 3 {s+1}\\ [4pt] (s^2-4s)Y (s ...

Nov 17, 2014 · Hint: Rather than gathering the terms in 10r 10 r together as you have, try first summing 10n−1 + 10n−2 +⋯+1 10 n 1 + 10 n 2 + + 1 as a geometric progression - which should give you a …

Aug 14, 2015 · A nice and quick way to visualize integration by parts (it could be a time-saver!): $$\matrix {&\text {differentiate}&&& &\text {integrate}&\\ &x^3&&&&e^x ...

Dec 14, 2019 · You can reach the gereral solution by integrating the given ODE repeatedly. Indeed, one has \begin {align*} & y'' - 4y' + 4 = x + 3e^ {2x} \Longleftrightarrow (y ...

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

Feb 3, 2016 · Evaluation of $\int_ {0}^ {\infty}t^3e^ {-3t}dt$ Ask Question Asked 9 years, 10 months ago Modified 9 years, 10 months ago