Nov 7, 2021 · Find the general solution to $xy' = 2y + x^3e^x$ Ask Question Asked 4 years, 1 month ago Modified 4 years, 1 month ago

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Sep 9, 2024 · You used a substitution, and then integration by parts once. But what if you start out with integration by parts? $$ \begin {align} \int x^3e^ {-x^2}\,dx &=\int -\frac12x^2\left (-2xe^ { …

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 ...

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.

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 ...

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.

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

Oct 2, 2020 · Is $y'''-3e^ty''- y'=t$ a linear differential equation or a nonlinear differential equation? I know the distinction between a linear D.E and nonlinear D.E but I am confused about this particular …

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 ...