Advanced Math Archive: Questions from May 27, 2023
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Sea \( D \) la región acotada por el eje \( y \) y la parábola \( x=-4 y^{2}+3 \). Halle \( \iint_{D} x^{3} y \mathrm{~d} x \mathrm{~d} y \).2 answers -
En los siguientes ejercicios, calcule \( \int_{\gamma} f \mathrm{~d} s \). (i) \( f(x, y)=e^{x+3 y} \) donde \( \gamma \) es el segmento rectilíneo en \( \mathbb{R}^{2} \) que va de \( (0,0) \) a \(2 answers -
Demuestre que el campo \( \mathbf{F}: \mathbb{R}^{4} \rightarrow \mathbb{R}^{4} \), dado por \[ \mathbf{F}(x, y, z, t)=\left(4 t x y+3 y z, 2 t x^{2}+3 x z, 3 x y+3 t^{2} z^{2}, 2 x^{2} y+2 t z^{3}\ri2 answers -
Calcule \( \int_{\mathbf{c}} \mathbf{F} \cdot \) ds de manera directa y usando el teorema de Stokes para \( \mathbf{F}(x, y)=\left(\frac{2 x}{x^{2}+y^{\prime}}, \frac{1}{x^{2}+y}\right) \), donde \( \2 answers -
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b) Solve the given initial value problem. \[ \begin{array}{ll} y^{\prime \prime}-64 y=16, & y^{\prime \prime}+y=8 \cos 2 x-4 \sin x \\ y(0)=1, y^{\prime}(0)=0 & y\left(\frac{\pi}{2}\right)=-1, y^{\pri2 answers -
find all lie point symmetries using X^[2] and X^[1]
\( y^{\prime \prime}+\frac{2}{x} y^{\prime}+y^{5}=0 \)2 answers -
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all the processes
Solve the IVP \[ \begin{array}{l} y^{\prime \prime}-6 y^{\prime}+9 y=0 \\ y(0)=5, \quad y^{\prime}(0)=9 \end{array} \]2 answers