Advanced Math Archive: Questions from June 21, 2023
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Solve the equation by separation of variables. \[ \begin{array}{l} y^{\prime}=\frac{x^{2}}{y\left(3-x^{3}\right)} \\ y= \pm \sqrt{-\frac{2}{3} \ln \left|3-x^{3}\right|+C} \\ y=\sqrt{\ln \left|3-x^{3}\2 answers -
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Calculate the double integral. \[ \iint_{R} x \sec ^{2}(y) d A, \quad R=\left\{(x, y) \mid 0 \leq x \leq 6,0 \leq y \leq \frac{\pi}{4}\right\} \]2 answers -
Si \( x=c_{1} \) cost \( +c_{2} \) sent es una solución de \( x^{\prime \prime}+x=0 \), halle la solución al problema de valor inicial de la ecuación diferencial dada las condiciones iniciales. a)2 answers -
8. \( f: R \subseteq \mathbb{R}^{n} \longrightarrow \mathbb{R} \) es continua. Probar we existe \( \bar{y} \in R \) tal que \[ \int_{R} f=f(\bar{y}) V(R) \]0 answers -
Resolver la siguiente ecuación con el método de Heun con 4 iteraciones \( y^{\prime}+1.5 y= \) \( 8 e^{0.5 x} \), comparando con la solución analítica y numérica según los valores iniciales \( x2 answers -
Find the general solution. (a) \( y^{\prime \prime \prime}-y^{\prime \prime}-6 y^{\prime}+6 y=0 \) (b) \( y^{(6)}-81 y=0 \)2 answers -
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