Advanced Math Archive: Questions from September 15, 2022
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please help me solve
Euler's method \( \begin{array}{llll}1 & y^{\prime}=2 x-y & x=0, y=1 & x=0(0 \cdot 2) 1 \cdot 0 \\ 2 & y^{\prime}=2 x+y^{2} & x=0, y=1 \cdot 4 & x=0(0 \cdot 1) 0 \cdot 5\end{array} \) Euler-Cauchy met1 answer -
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2.Solve the initial-value problem (IVP) \[ y^{\prime}=\sec \left(\frac{y}{x}\right)+\frac{y}{x} \quad, \quad y(1)=\frac{\pi}{2} . \]1 answer -
2.Solve the initial-value problem (IVP) \[ (\tan y-2) d x+\left(x \sec ^{2} y+\frac{1}{y}\right) d y=0, y(0)=1 . \]1 answer -
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Please do letter "B" and explain the answer
Dados los siguientes conjuntos \( \mathrm{A}=\{\mathrm{a}, \mathrm{e}, i, 6,8,9\} \quad \mathrm{B}=\{\mathrm{a}, \mathrm{i}, \mathrm{o}, 1,2,3\} \quad \mathrm{C}=\{\mathrm{a}, \mathrm{e}, \mathrm{u},1 answer -
\( y^{i v}+4 y=0, y(0)=\frac{1}{2}, y^{\prime}(0)=-\frac{3}{2}, y^{\prime \prime}(0)=\frac{5}{2}, y^{\prime \prime \prime}(0)=\frac{-7}{2} \)1 answer -
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5. Solve the initial value problem \[ \left[2 \cos (2 x+y)-x^{2}\right] d x+\left[\cos (2 x+y)+e^{y}\right]=0, y(1)=0 \]1 answer -
Differentiate the following to \( x \) and simplify where possible: 2.1 \( y=x^{4} \tan 3 x \) \( 2.2 \quad y=\ell n\left(2 x^{2}+1\right) \) \( 2.3 \quad y=\frac{e^{x}+1}{e^{x}-1} \) \( 2.4 y=\frac{22 answers -
Find the general solution of \[ y^{\prime}=\frac{2 x^{7} e^{y / x}+x^{5} y^{2}}{x^{6} y} \] a) \( y=\ln \left(\frac{x+y}{C x-x \ln \left(x^{2}\right)}\right) \) b) \( y=x \ln \left(\frac{x+y}{C x-x \l1 answer -
13. Maximize \( z=5 x+2 y \) subject to: \[ \begin{aligned} 4 x-y & \leq 16 \\ 2 x+y & \geq 11 \\ x & \geq 3 \\ y & \leq 8 \end{aligned} \]1 answer -
\[ y^{i v}+4 y=0, y(0)=\frac{1}{2}, y^{\prime}(0)=-\frac{3}{2}, y^{\prime \prime}(0)=\frac{5}{2}, y^{\prime \prime \prime}(0)=\frac{-7}{2} \] Solve the ODE2 answers -
Tiempo restante de la secodn: Instrucciones: Para cada una de las siguientes preguntas marque la opción que considere correcta. 24.SI una fábrica puede producir 15 bicicletas por hora, entonces prod1 answer -
\[ y^{i v}+4 y=0, y(0)=\frac{1}{2}, y^{\prime}(0)=-\frac{3}{2}, y^{\prime \prime}(0)=\frac{5}{2}, y^{\prime \prime \prime}(0)=\frac{-7}{2} \] Solve the ODE1 answer -
\[ y^{i v}+4 y=0, y(0)=\frac{1}{2}, y^{\prime}(0)=-\frac{3}{2}, y^{\prime \prime}(0)=\frac{5}{2}, y^{\prime \prime \prime}(0)=\frac{-7}{2} \] Solve the ODE1 answer -
(1 point) Find an explicit general solution for 1) \( y^{\prime}=\frac{2}{x} \Rightarrow y= \) \( +C \) 2) \( y^{\prime}=-3 \sin x+4 \cos x \Rightarrow y= \) 3) \( y^{\prime}=-6 e^{x} \Rightarrow y= \1 answer -
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 -
number 23 please
In Exercises 19-26, solve the Initial Value Problem. 19. \( y^{\prime}+3 y=e^{2 x}, \quad y(0)=-1 \) 20. \( x y^{\prime}+y=e^{x}, \quad y(1)=3 \) 21. \( y^{\prime}+\frac{1}{x+1} y=x^{-2}, \quad y(1)=21 answer -
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iven \( y=2 e^{3 x}+4 x^{3} \) \[ 6 e^{2 x}+12 x^{2} \] \[ 6 e^{3 x}+12 x^{2} \] \[ 2 e^{3 x}+24 x \] \[ 18 e^{3 x}+24 x \]1 answer -
Find the general solution for the ordinary differential equation \( y^{\prime \prime}+9 y=0 \) \[ y=A \cos 3 x+B \sin 3 x \] \[ y=(A+B x) e^{3 x} \] \[ y=(A+B x) e^{-3 x} \] \[ y=e^{x}(A \cos 3 x+B \s1 answer -
Find \( \mathrm{y}^{\prime} \), given \( y=\ln x \cos x \) \[ \begin{aligned} y^{\prime} &=\frac{\cos x}{x}+\sin x \ln x \\ y^{\prime} &=-\frac{\sin x}{x} \\ y^{\prime} &=\frac{\sin x}{x} \\ y^{\prime1 answer -
iven \( y^{\prime}=6 x^{5}-2 \pi \) \[ y=30 x^{4} \] \( y=30 x^{4}+c \) \[ y=x^{6}+c \] \[ y=x^{6}-2 \pi x+c \]1 answer