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 ...

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, 4 months ago Modified 4 years, 4 months ago

Feb 18, 2015 · I know this is true: $$ \lim_ {x \to 0}\frac {e^ {x}-1} {x} = 1 $$ So I've tried to isolate the $5x$ so that $ (1/5)$ multiplies by all of it. Then I'm not sure what to do.

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 ...

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 solutions for each …

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 independently?

Nov 4, 2011 · You'll need to complete a few actions and gain 15 reputation points before being able to upvote. Upvoting indicates when questions and answers are useful. What's reputation and how do I …

May 11, 2021 · So I was given the following prompt: "For the following, use the definition to find the Taylor (or Maclaurin) series centered at c for the function. When writing your answers, be sure to list ...