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

Jul 14, 2016 · the area is $|a\land b|=|-5e_1 \land e_2 + 10e_1 \land e_3 + 5e_2 \land e_3|=\sqrt { (-5)^2 + 10^2 + 5^2}=5\sqrt {6}$

I am not sure how I am suppose to do this so I set it up normally. ∫z3ez ∫ z 3 e z u= z3dx u = z 3 d x du= 3z2 d u = 3 z 2 dv= ez d v = e z v = ez v = e z ezz3 −∫ez3z2 e z z 3 ∫ e z 3 z 2 This then leads to a …