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Advanced Math Archive: Questions from February 22, 2023

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  \( \frac{6 x^{2}-x y-y^{2}}{2 x^{2}+x y-y^{2}} \div \frac{16 y^{2}-4 x^{2}}{2 x^{2}+6 x y+4 y^{2}} \)
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  \( \frac{6 x^{2}-x y-y^{2}}{2 x^{2}+x y-y^{2}} \div \frac{16 y^{2}-4 x^{2}}{2 x^{2}+6 x y+4 y^{2}} \)
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  3. Solve the following differential equations. (a) \( 9 y^{(4)}-6 y^{(3)}+y^{(2)}=0 \) (b) \( y^{\prime \prime}-4 y^{\prime}+5 y=0 \) (c) \( y^{\prime \prime}-3 y^{\prime}+2 y=3 e^{-x}-10 \cos 3 x, y(
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  2. Prove: \( \forall x \in \mathbb{R}, \exists y \in \mathbb{R}_{\ni} x^{3}=y \).
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  Uno de los valores de \( y=x^{m} \) que es solución para \( x^{2} \frac{d^{2} y}{d x^{2}}-7 x \frac{d y}{d x}+12 y=0 \) es \( m=-3 \)
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  uestion 2 La ecuación \( x \frac{d y}{d x}-3 x y=\sin x \) una ecuación lineal de primer orden
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  2. Solve the following EXACT differential equations. (a) \( (\sin y+y \cos x) d x+[\sin x+x \cos y] d y=0 \) (b) \( \frac{y}{x} d x+(1+\ln (x y)) d y=0 \)
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  Express the integral \( \iiint_{E} f(x, y, z) d V \) as an iterated integral in six different ways, where \( \mathrm{E} \) is the solid bounded by \( z=0, z=2 y \) and \( x^{2}=1-y \). 1. \( \int_{a}^
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  A Vorng to mane ancten we gava tha resocnse. iestinn La ecuación \( x \frac{d y}{d x}-3 x y=\sin x \) una ecuación lineal de primer orden
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  Uno de los valores de \( y=x^{m} \) que es solución para \( x^{2} \frac{d^{2} y}{d x^{2}}-7 x \frac{d y}{d x}+12 y=0 \) es \( m=-3 \) put riis
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  \( \frac{d y}{d r}- \) ey \( \sin x \) no et wne coucsiond ineal True rume
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• Taylor Series.
  Find \( T_{3}(\mathbf{X}) \). (a) \( f(x, y)=e^{x} \cos y, \quad \mathbf{X}_{0}=(0,0) \) (b) \( f(x, y)=e^{-x-y}, \quad \mathbf{X}_{0}=(0,0) \) (c) \( f(x, y, z)=(x+y+z-3)^{5}, \quad \mathbf{X}_{0}=(1
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  Encontremos los valores extremos de \( f(x, y, z)=3 x-y-3 z \) sujeto a las siguientes restricciones \( g_{1}(x, y, z)=x+y-z=0 \) y \( g_{2}(x, y, z)=x^{2}+2 z^{2}-1=0 \). 1. La condicion (restriccion
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  Q2. (10 pts )Solve the following a. \( y^{\prime}=2 x+5 y, \quad y(0)=3 \)
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  2. Prove: \( \forall x \in \mathbb{R}, \exists y \in \mathbb{R}_{\ni} x^{3}=y \).
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• Help with question 18 please.
  Solving Initial Value Problems. Solve the initial problems in Exercise Group 4.2.7.17-24. 17. \( y^{\prime \prime}-2 y^{\prime}-3 y=3 e^{2 t}, y(0)=1, y^{\prime}(0)=0 \) 18. \( y^{\prime \prime}-y^{\p
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• Help with question 20
  Solving Initial Value Problems. Solve the initial problems in Exercise Group 4.2.7.17-24. 17. \( y^{\prime \prime}-2 y^{\prime}-3 y=3 e^{2 t}, y(0)=1, y^{\prime}(0)=0 \) 18. \( y^{\prime \prime}-y^{\p
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• help with question 22
  Solving Initial Value Problems. Solve the initial problems in Exercise Group 4.2.7.17-24. 17. \( y^{\prime \prime}-2 y^{\prime}-3 y=3 e^{2 t}, y(0)=1, y^{\prime}(0)=0 \) 18. \( y^{\prime \prime}-y^{\p
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  Solve the following Bernoulli differential equations: 1. \( y^{\prime}+y=x e^{x} \sqrt{y}, \quad y(0)=4 \) 2. \( y^{\prime}-(\tan x) y=(\cos x) y^{4}, \quad y(0)=3 \)
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  Halle \( \cot \theta \) para \( \theta \) en posición estándar y su lado terminal pasa por el punto \( P(-2,7) \).
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• show using the additive and homogenity property
  Which of the following is a matrix transformation. (A) \( T(x, y, z)=\left(y x^{2}, y z^{2}\right) \) (B) \( T(x, y, z, w)=(y x, y z, z w, w x) \) (C) \( T(x, y, z)=(x+1, x+2, x+z, y+z) \) (D) \( T(x,
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  7. True or false: \[ \oint_{|z|=1} \bar{z} d z=\oint_{|z|=1} \frac{1}{z} d z \]
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• Use the appropriate sum or difference ide cos2u=cos^(2)u-sin^(2)u
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