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Advanced Math Archive: Questions from July 19, 2022

• Hand writing pls
  Q4. Determine the Fourier transform of \( g(y)=e^{-4 y} \) if \( y>0 \) and \( g(y)=0 \) if \( y
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  Q4. Determine the Fourier transform of \( g(y)=e^{-4 y} \) if \( y>0 \) and \( g(y)=0 \) if \( y
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  4. Find the domain and the range for the following functions. a. \( f(x, y, z)=x+y-z \) b. \( f(x, y, z)=z-\sqrt{x^{2}+y^{2}} \) c. \( f(x, y, z)=z-x^{2}-y^{2} \) d. \( f(x, y, z)=\sqrt{25-x^{2}-y^{2}
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• Solve the Initial value prob: y" - 6y' + 9y = 0, y(0) = 0, y'(0) = 2
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  \( \mathcal{L}=1\left\{\ln \left(1+\frac{1}{s}\right)\right\} \) b) \( \int_{0}^{1} y(u) y(t-u) d u=\frac{1}{2}[\sin (t)-t \cos (t)] \)
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  Find \( Y(s) \) for the initial value problem \[ y^{\prime \prime}-25 y=g(t), y(0)=5, y^{\prime}(0)=3, g(t)=\left\{\begin{array}{ll} 4 & t5 \end{array}\right. \]
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  Solve \[ y^{\prime}(t)+y(t)-\int_{0}^{t} \sin (t-v) y(v) d v=-7 \sin t, y(0)=7 \]
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  ( 1 point) Find \( y \) as a function of \( x \) if \[ y^{\prime \prime \prime}-13 y^{\prime \prime}+40 y^{\prime}=28 e^{x}, \] \[ \begin{array}{l} y(0)=30, y^{\prime}(0)=16, y^{\prime \prime}(0)=16 .
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  Calcule \( f(4) \) con Newton Interpolación de nimeros de segundo y tencer grodo \[ x_{n-1}=\left(\frac{f\left(x_{n}\right)-f\left(x_{0}\right)}{v}\right)+\left(\frac{f\left(x_{2}\right)-f\left(x_{2}
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  c) \( \int_{C} z, x, y \bullet d \vec{r} \) donde \( C: \boldsymbol{r}(t)=a \cos (t) \boldsymbol{i}+a \operatorname{sen}(t) \boldsymbol{j}+t \boldsymbol{k} ; \operatorname{con} t \in[0,2 \pi] \). Answ
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  Suppose that \( R=\{(x, y): 0 \leq x \leq 3,0 \leq y \leq 3\} \), \( R_{1}=\{(x, y): 0 \leq x \leq 3,0 \leq y \leq 2\} \), and \( R_{2}=\{(x, y): 0 \leq x \leq 3,2 \leq y \leq 3\} \). Suppose, in addi
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  Resolver la siguiente integral: \[ \int_{-\infty}^{+\infty}|x| \cdot e^{-x^{2}} \cdot d x \]
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  Verificar que la función \( y=e^{x} \cdot \int_{0}^{x} e^{t^{2}} \cdot d t+c e^{x} \quad \) satisface la siguiente ecuación Diferencial \( \frac{d y}{d x}-y=e^{x+x^{2}} \)
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  Determinar si la siguiente ecuación diferencial es una ecuación diferencial exactas, si es encuentre la función \( f(x ; y) \). \[ y\left(e^{x y}+y\right) \cdot d x^{\prime}+x\left(e^{x y}+2 y\righ
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• need 20 solved
  In Problems 15-24, solve for \( Y(s) \), the Laplace transform of the solution \( y(t) \) to the given initial value problem. 15. \( y^{\prime \prime}-3 y^{\prime}+2 y=\cos t ; \quad y(0)=0, \quad y^{
  2 answers
• need 28 solved
  In Problems 25-28, solve the given third-order initial value problem for \( y(t) \) using the method of Laplace transforms. 25. \( y^{\prime \prime \prime}-y^{\prime \prime}+y^{\prime}-y=0 \); \( y(0)
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  Using Laplace Transform to solve the following equations: (a) \( y^{\prime \prime}+3 y^{\prime}+2 y=e^{t}, \quad y(0)=0, y^{\prime}(0)=1 \) (b) \( y^{\prime \prime}+5 y=\sin 2 t, y(0)=y^{\prime}(0)=0
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