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Advanced Math Archive: Questions from July 20, 2022

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  Problem 1: \[ y^{\prime} \sqrt{1+x+y}=x+y-1 \] Problem 2: \[ y^{\prime}=\cos (x-y) \]
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  Solve the initial-boundary value problem \[ \begin{array}{l} \frac{\partial u}{\partial t}=9 \frac{\partial^{2} u}{\partial x^{2}} \text { for } 0
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• differential equations 1) resolve the next linear equation: 2) determine whether the functions are LI or LD in[0,♾️] hint: use the formula
  1) Resuelva la siguiente ecuación lineal \( \frac{d y}{d x}+y=\frac{1}{e^{x}+e^{-x}} \) 2) Determine si las funciones son L.I o son L.D en \( [0, \infty] \) Sugerencia: Use la formula \( \operatornam
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• 2) determine if the functions are LI or LD on [0,♾️] hint: use the formula sin(2x)=2sen(x).cos(x) 3) if the solution is a differential equation, obtain the other solution using Abel's formula
  2) Determine si las funciones son L.I o son L.D en \( [0, \infty] \) Sugerencia: Use la formula \( \operatorname{sen}(2 x)=2 \operatorname{sen} x \cos x \) 3) \( \mathrm{Si} \) es una solución de la
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• 4) solve the following differential equation +6 must appear all synthetic divisions 5) use the parameter variation method
  4) Resuelva las siguientes ecuaciones diferenciales: a) \( y^{5}-16 y^{\prime}=0 \) b) \( y^{(5)}+6 y^{(4)}+15 y^{\prime))}+26 y^{\prime)}+36 y^{3}+24 y=0 \). Deben aparecer todas las divisiones sint�
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• diferencials equation
  PRACTICA 2 1) Resuelva la siguiente ecuación lineal \( \frac{d y}{d x}+y=\frac{1}{e^{x}+e^{-x}} \) differential equations 1) resolve the next linear equation:
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• diferencial equation
  2) Determine si las funciones \( f(x)=\cos 2 x, g(x)=1, h(x)=\cos ^{2} x \) son L.I o son L.D en \( [0, \infty] \) Sugerencia: Use la formula \( \operatorname{sen}(2 x)=2 \operatorname{sen} x \cos x \
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• solve the following differential equations: must appear all synthetic divisions
  4) Resuelva las siguientes ecuaciones diferenciales: a) \( y^{5}-16 y=0 \) b) \( \left.y^{(5)}+6 y^{(4)}+15 y^{\prime))}+26 y^{\prime}\right)+36 y^{\prime}+24 y=0 \).
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• use the parameter variation method
  5) Use el método de variación de parámetros \[ \left.y^{y}\right)-2 y^{\prime}+2 y=e^{x} \sec x \]
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• please solve 17
  In Problems 17-22, find a general solution to the differ ential equation. 17. \( y^{\prime \prime}-y=-11 t+1 \) 18. \( y^{\prime \prime}-2 y^{\prime}-3 y=3 t^{2}-5 \) 19. \( y^{\prime \prime}(x)-3 y^{
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• Find the inverse function of function .
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• Only 71
  In Problems 65-72 solve the given initial-value problem. 65. \( y^{\prime \prime}-64 y=16, \quad y(0)=1, y^{\prime}(0)=0 \) 66. \( y^{\prime \prime}+y^{\prime}=x, \quad y(0)=1, y^{\prime}(0)=0 \) 67.
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  If \( \sin \theta=\frac{4}{9}, 0
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• The value of the integral ... where f: ... and the curve £ is given by the intersection of the surfaces: ... *suggestion: parameterize the curve* The instructions have been translated, hope it
  El valor de la integral \( \int_{\zeta} f d s \) donde \( f: \mathbb{R}^{3} \rightarrow \mathbb{R}, f(x, y, z)=x^{2}+2 y^{2} \), y la curva \( \zeta \) está dada por la intersección de las superfici
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• Let S be a surface given by the parameterization r(u, v) = (u, v, uv), where 0 <= u <= 1; and 0 <= v <= 2. The value of I = ... is equal to:
  Sea \( S \) la superficie dada por la parametrización \( \vec{r}(u, v)=(v, u, u v) \), donde \( 0 \leq u \leq 1 ; 0 \leq v \leq 2 \). El valor de \( I=\iint_{S} \frac{1}{\sqrt{1+x^{2}+y^{2}}} d S \)
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• Let 𝐼=, where C is the curve with parameterization 𝛼(𝑡)=(sin(4𝑡),cos(4𝑡)), with 0≤𝑡≤𝜋16. In reference to the value of 𝐼, it is correct to state that: a) 𝐼=1 b) none c)
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• SOLVE THE IVP
  \( y \cos x-2 x e^{y}-6 x^{2}-\left(x^{2} e^{y}-\sin x-4\right) y^{\prime}=0 ; \quad y(\pi)=0 \)
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• Resolve. Show the entire process plis.
  1. \( 2 \operatorname{sen}^{2} \Theta-3 \operatorname{sen} \Theta+1=0 \quad 0 \leq \Theta \leq 2 \pi \) 2. \( 2 \cos \Theta=1 \) \( 0 \leq \Theta \leq 2 \pi \) B. Establezca la identidad. \[ \frac{1-\
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• NOTE: PLEASE SOLVE USING ANNIHILATORS METHOD PLEASE!!
  1. Solve the following non-homogeneous differential equations with constant coefficients: a) \( y^{\prime \prime}-y=9 x e^{2 x}, y(0)=0, y^{\prime}(0)=7 \) b) \( y^{\prime \prime}+4 y^{\prime}+4 y=169
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  Problem 7 (16 points). Solve the following IVP: \[ y \cos x-2 x e^{y}-6 x^{2}-\left(x^{2} e^{y}-\sin x-4\right) y^{\prime}=0 ; \quad y(\pi)=0 \]
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• Please solve using annihilators if possible!!!
  \( y^{\prime \prime}+16 y=34 e^{x}+16 \cos 4 x-8 \sin 4 x \)
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