calculus - Integration by Parts Question: Integrate $x^3e^x ...
Aug 14, 2015 · A nice and quick way to visualize integration by parts (it could be a time-saver!): $$\matrix {&\text {differentiate}&&& &\text {integrate}&\\ &x^3&&&&e^x ...
Problems finding particular solution for $y''-4y'+4y=x+3e^{2x}$
Dec 14, 2019 · You can reach the gereral solution by integrating the given ODE repeatedly. Indeed, one has \begin {align*} & y'' - 4y' + 4 = x + 3e^ {2x} \Longleftrightarrow (y ...
Solving $\int_0^ {\infty}x^3e^ {-x^2}dx$ [duplicate]
Sep 9, 2024 · Solving $\int_0^ {\infty}x^3e^ {-x^2}dx$ [duplicate] Ask Question Asked 1 year, 5 months ago Modified 1 year, 5 months ago
Find the general solution to $xy' = 2y + x^3e^x$
Nov 7, 2021 · Find the general solution to $xy' = 2y + x^3e^x$ Ask Question Asked 4 years, 3 months ago Modified 4 years, 3 months ago
Use Laplace Transformations to solve $y''+2y'+5y=3e^{-x}sin(x)$, …
Apr 12, 2016 · Start asking to get answers Find the answer to your question by asking. Ask question
If the Wronskian W of $f$ and $g$ is $3e^{4t}$, and if $f(t) = e^{2t ...
If you simplify by factoring out $e^ {2t}$ and cancelling, that would give you $$g' - 2g = 3e^ {2t},$$ instead of $g'-2g = 3e^ {4t}$, which is what you had. So it looks like you made a simplification …
Evaluate: $\int\frac {3e^ {2x}-2e^x} {e^ {2x}+2e^x-8}dx$
Feb 21, 2023 · (+1) @StrawberryVanilla: note that $\frac {\left|e^ {2x}+2e^x-8\right|^ {\frac32}} {\left|\frac {e^x-2} {e^x+4}\right|^ {\frac56}}=|u-2|^ {\frac32-\frac56}|u+4 ...
calculus - (Laplace Method) $y'' - 4y' = 6e^ {3t} - 3e^ {-t ...
Apr 8, 2016 · Taking the Laplace Transform to both sides of the ODE we get \begin {align*} s^2Y (s)-s (1)- (-1)-4 [sY (s)-1]&=\frac 6 {s-3}-\frac 3 {s+1}\\ [4pt] (s^2-4s)Y (s ...
calculus - How to solve $y''+4y=e^x\cos2x+3e^ {3x}
You can do that with every linear ODE. If L(y) = 0 L (y) = 0 is the homogeneous equation, with L L as the differential operator, here L = d2 dx2 + 4 L = d 2 d x 2 + 4, and you have particular …
linear algebra - Differentiating and integrating $r (t)=\langle 8t^4 ...
Nov 25, 2020 · I am asked to differentiate and integrate $$r (t)=\langle 8t^4+\frac {5} {t} ,\sec^2 (\frac {t\pi} {6},3e^t-2t\ln (t))\rangle $$ Am I supposed to differentiate/integrate each term …