Advanced Math Archive: Questions from September 16, 2022
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Solve the differential equation \( \frac{d y}{d x}-6 x^{2}=2, y(1)=6 \) \[ y=2 x^{3}+6 \] \[ y=12 x-6 \] \[ y=2\left(x^{3}+x+1\right) \] \[ y=2 x^{3}+a x+2 \]1 answer -
Solve the differential equation \( \frac{d y}{d x}-6 x^{2}=2, y(1)=6 \) \[ y=2 x^{3}+6 \] \[ y=12 x-6 \] \[ y=2\left(x^{3}+x+1\right) \] \[ y=2 x^{3}+a x+2 \]1 answer -
Find a particular solution for the differential equation. \[ \begin{array}{l} \left(72 x^{2}-14 x\right) d x-d y=0 ; y=-5 \text { when } x=0 \\ y=72 x^{3}-7 x^{2}-5 \\ y=72 x^{3}-14 x^{2}-5 \\ y=24 x^1 answer -
Find the anti-derivative of \( 6 \sin (2 x)(\cos 2 x)^{2} \) \[ -2(\cos 2 x)^{3}+c \] \[ y=(\cos 2 x)^{3}+c \] \[ y=-(\cos 2 x)^{3}+c \] \[ y=2(\cos 2 x)^{3}+c \]2 answers -
Sea \( y_{i}(x)=x^{2} \cos (\ln x) \) una solución de la ecuación diferencial \( x^{2} y^{\prime \prime}-3 x y^{\prime}+5 y=0 \). Encuentre una segunda solución. \[ y_{2}(x)=x^{2} \tan (\ln x) \] \1 answer -
Encuentre la solución general de la ecuación diferencial \( \frac{d^{3} t}{d s^{5}}+5 \frac{d^{4} t}{d s^{4}}-2 \frac{d^{3} t}{d s^{3}}-10 \frac{d^{2} t}{d s^{2}}+\frac{d t}{d s}+5 t=0 \). \[ t=c_{11 answer -
solve ( v , vi , viii )
Problem 2 Solve the following differential equations by using power series solutions around singular points \( x=0 \). (i) \( 2 x y^{\prime \prime}-y^{\prime}+2 y=0 \). (ii) \( x y^{\prime \prime}-x y1 answer -
Solve \( \frac{y}{x} \cos \left(\frac{y}{y}\right)-\left[\frac{y}{x} \sin \left(\frac{y}{v}\right)+\cos \left(\frac{y}{x}\right)\right] \frac{d y}{d x}=0 \) a. \( y \cos \left(\frac{y}{x}\right)=c x \2 answers -
1.) SOLVE THIS FOLLOWING HOMOGENOUS DIFFERENTIAL EQUATION A.) \( \quad v^{2} d x+x(x+v) d v=0 \) B.) \( \quad(x-y \ln y+y \ln x) d x+x(\ln y-\ln x) d y=0 \).1 answer -
22. For the following matrix \[ \Sigma=\left[\begin{array}{cccc} 1.21 & -1.04 & 0.79 & -0.81 \\ -0.72 & 0.73 & 0.89 & 2.99 \\ 1.63 & 0.31 & -1.15 & -1.44 \\ 0.49 & 0.29 & 1.07 & -0.33 \end{array}\righ2 answers -
22. For the following matrix \[ \Sigma=\left[\begin{array}{cccc} 1.21 & -1.04 & 0.79 & -0.81 \\ -0.72 & 0.73 & 0.89 & 2.99 \\ 1.63 & 0.31 & -1.15 & -1.44 \\ 0.49 & 0.29 & 1.07 & -0.33 \end{array}\righ1 answer -
Situation: A student with an influenza virus returns to an isolated college campus with a thousand students. Assuming that the rate at which the virus spreads is proportional not only to the number x
Situación: Un estudiante portador de u virus de influenza regresa a un campus universitario aislado que tiene mil estudiantes. Si se supone que la rapidez con que el virus se propaga es proporcional1 answer -
1 answer
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9. Una lancha, que viaja a \( 20 \mathrm{~m} / \mathrm{s} \), pasa por debajo de un puente 3 segundos después que ha pasado un bote, que viaja a \( 16 \mathrm{~m} / \mathrm{s} \). ¿Después de cuán1 answer -
Find the potential function f for the field F. \[ \begin{array}{l} F=\left\{-\frac{1}{x}, \frac{1}{y},-\frac{1}{z}\right\} \\ f(x, y, z)=\ln \left(\frac{y}{x z}\right) \\ f(x, y, z)=\frac{1}{x^{2} y^{1 answer -
/classify ODEs: (1) \( y^{\prime \prime}+2 y^{\prime}+e^{y}=x \) (2) \( 3 x^{2} y^{\prime \prime}+2 \ln (x) y^{\prime}+e^{x} y=3 x \cos x \)1 answer -
classify ODES
(3) \( 4 y y^{\prime \prime}-x^{3} y^{\prime}+\cos y=e^{2 x} \) (4) \( \frac{d^{2} y}{d x^{2}}+\frac{d y}{d x}=3 x \sin y \) (3) \( 4 y y^{\prime \prime}-x^{3} y^{\prime}+\cos y=e^{2 x} \) (4) \( \fr1 answer -
1 answer
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Find the gradient of the following functions. a) \( \quad f(x, y, z)=3 x^{2} \sqrt{y}+\cos (3 z) \) b) \( \quad g(x, y, z)=\sin (3 x) e^{2 y} \ln (4 z) \)1 answer -
Si los vectores \( u \) y \( v \) están definidos en \( R^{4} \) por \( u=(1,-1,0,1) \) y \( v=(0,2,3,-1) \), resuelva para \( w \) en \( w+3 v=-2 u \) a. \( (2,-3,9,-1 \) b. \( (1,-3,9,-5) \) c. \(1 answer