Advanced Math Archive: Questions from October 30, 2023
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use Frobenius method, y" + 1/x y' - 1/x^2 y = 0
\[ y^{\prime \prime}+\frac{1}{x} y^{\prime}-\frac{1}{x^{2}} y=0 \quad, \quad \begin{array}{l} b(x)=1, c(x)=-1 \\ \text { analytic } \end{array} \] ube Frobenius methad and solve this Eq1 answer -
\( \sin \frac{\pi}{12} \cos \frac{\pi}{4}-\cos \frac{\pi}{12} \sin \frac{\pi}{4} \) \( \frac{\tan \frac{\pi}{3}+\tan \frac{\pi}{4}}{1-\tan \frac{\pi}{3} \tan \frac{\pi}{4}} \) \( \left(\cos \frac{\pi}1 answer -
please solve #3
3) \( y^{\prime \prime}-2 y^{\prime}-3 y=3 x e^{2 x}, \quad y(0)=y^{\prime}(0)=1 \) 4) \( y^{\prime}+2 y^{\prime}+5 y=4 e^{-x} \cos (2 x), \quad y(0)=1, \quad y^{\prime}(0)=0 \)1 answer -
please solve #4
3) \( y^{\prime \prime}-2 y^{\prime}-3 y=3 x e^{2 x}, \quad y(0)=y^{\prime}(0)=1 \) 4) \( y^{\prime}+2 y^{\prime}+5 y=4 e^{-x} \cos (2 x), \quad y(0)=1, \quad y^{\prime}(0)=0 \)1 answer -
Use the handshaking lemma to evaluate \( \left|E\left(K_{\alpha}\right)\right| \) for all \( \alpha \in \mathbb{N}^{*} \).1 answer -
Actividad 6 a) Hallar una solución particular sin calcular los coeficientes A, de las siguientes ED. y" - 2y + 2y = 5te cos(t) y" - 2y + y = 1²et y" + 2y + 2y = 5e-tsin(t) + 5t³e-cos(t) y" -y = e²
Hallar una solución particular sin calcular los coeficientes \( A_{j} \) de las siguientes ED. \[ \begin{array}{l} y^{\prime \prime}-2 y^{\prime}+2 y=5 t e^{t} \cos (t) \\ y^{\prime \prime}-2 y^{\pri1 answer -
( 1 point) Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 2 x \cos y+5 \sin 21 answer -
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En cierta fábrica, el costo de fabricar q unidades durante la jornada de producción diaria es \( C(q)=0.2 q^{2}+q+900 \) dólares. Con base a la experiencia se ha determinado que aproximadamente \(1 answer -
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Solve \[ \begin{array}{ll} x^{\prime}=y & x(0)=0 \\ y^{\prime}=12 x+1 y & y(0)=8 \end{array} \] \[ x(t)= \] help (formulas) \[ y(t)= \] help (formulas)1 answer -
Solve \[ \begin{array}{ll} x^{\prime}=y & x(0)=0 \\ y^{\prime}=16 x+6 y & y(0)=8 \end{array} \] \[ \begin{array}{ll} x(t)= & \text { help (formulas) } \\ y(t)= & \text { help (formulas) } \end{array}1 answer -
Solve x(t) = y(t) = x' = y y = 15x + 2y help (formulas) help (formulas) x(0) = 0 y(0) = 2
Solve \[ \begin{array}{ll} x^{\prime}=y & x(0)=0 \\ y^{\prime}=15 x+2 y & y(0)=2 \end{array} \] \[ x(t)= \] help (formulas) \[ y(t)= \] help (formulas)1 answer -
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Solve the following initial value problems: 1. \[ \left\{\begin{array}{l} y^{\prime \prime}+y=25 x e^{2 x} \\ y(0)=0 \\ y^{\prime}(0)=1 \end{array}\right. \] 2. \[ \left\{\begin{array}{l} y^{\prime \p1 answer -
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(1 point) Find \( y^{\prime} \) by implicit differentiation. Match the equations defining \( y \) implicitly with the letters labeling the expressions for \( y^{\prime} \). 1. \( 6 x \cos y+4 \sin 2 y1 answer -
Solve \[ \begin{array}{ll} x^{\prime}=y & x(0)=0 \\ y^{\prime}=6 x+5 y & y(0)=2 \end{array} \] \[ x(t)= \] help (formulas) \[ y(t)= \] help (formulas)1 answer -
1 answer
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3. Determine all possible values of 0, where 0°≤ 0≤360°. Show all your work for full marks. (12) a) cose = 0.6951 b) sin sin 0 = 0.314 c) cot cot 0 = 8. 1516 d) tan tan 0 == 0.7571 e) sin sin 0
3. Determine all possible values of \( \theta \), where \( 0^{\circ} \leq \theta \leq 360^{\circ} \). Show all your work for full marks. (12) a) \( \cos \theta=0.6951 \) d) \( \tan \tan \theta=-0.75711 answer -
Solve \( \frac{d^{4} y}{d x^{4}}-y=0 \), where \( y(0)=1, y^{\prime}(0)=0, y^{\prime \prime}(0)=3 \) and \( y^{\prime \prime \prime}(0)=5 \).1 answer -
3. Find the total differential, given X1 X1 + X2 (a) y = (b) y = 2X1 X2 X1 + X2
3. Find the total differential, given (a) \( y=\frac{x_{1}}{x_{1}+x_{2}} \) (b) \( y=\frac{2 x_{1} x_{2}}{x_{1}+x_{2}} \)1 answer -
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17. Sean \( a_{1}, a_{2}, \ldots, a_{n} \) números positivos. Se definen \[ \begin{array}{c} a_{A}=\frac{1}{n} \sum_{i=1}^{n} a_{i}, \\ a_{G}=\left(\prod_{i=1}^{n} a_{i}\right)^{1 / n} \end{array} \]1 answer -
(1 point) Find d87 dx87 Answer: 3cos(3x) sin(3x).
\[ \text { (1 point) Find } \frac{d^{87}}{d x^{87}} \sin (3 x) \text {. } \] Answer:1 answer