Advanced Math Archive: Questions from February 23, 2023
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Solve the differential equation. 2) \( \frac{d y}{d x}=6 x \sqrt{9-y^{2}} \) A) \( y=3 \sin \left(3 x^{2}+C\right) \) B) \( y=3 \sin ^{-1}\left(3 x^{2}+C\right) \) C) \( y=\sin \left(3 x^{2}+C\right)2 answers -
11) \( \frac{d y}{d x}=e^{4 x-4 y} \) 11) A) \( y=4 e^{4 x}+C \) B) \( y=\ln \left(e^{4 x}+C\right) \) C) \( y=4 \ln \left(e^{4 x}+C\right) \) (D) \( y=\frac{1}{4} \ln \left(e^{4 x}+C\right) \)2 answers -
2 answers
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Solve the following DEs: No. 9.19. \( \quad y^{\prime \prime}-y=0 \). No. 9.19. \( \quad y^{\prime \prime}-2 y^{\prime}+y=0 \). No. 9.21. \( \quad y^{\prime \prime}+2 y^{\prime}+2 y=0 \)2 answers -
2 answers
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2 answers
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0 answers
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2 answers
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Solve for \( x \) and \( y \) in the matrix \( A=\left[\begin{array}{cc}x & 3 \\ -5 & y\end{array}\right] \) if \( A^{2}=\left[\begin{array}{cc}21 & 15 \\ -25 & -14\end{array}\right] \). \[ x= \] \[ y2 answers -
2 answers
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please help!
In each of Problems 8 through \( \underline{16} \), use the Laplace transform to solve the given initial value problem. 14. \( y^{(4)}-y=0 ; \quad y(0)=1, \quad y^{\prime}(0)=0, \quad y^{\prime \prim2 answers -
Answer number 2 please
Solve the following Bernoulli differential equations: 1. \( y^{\prime}+y=x e^{x} \sqrt{y}, \quad y(0)=4 \) 2. \( \quad y^{\prime}-(\tan x) y=(\cos x) y^{4}, \quad y(0)=3 \)2 answers -
Calculate all four second-order partial derivatives of \( f(x, y)=\sin \left(\frac{3 x}{y}\right) \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y)= \]2 answers -
need to know if the three are exact or not and why, help please!! Necesito saber si las 3 son exactas o no y por que cada una, por favor!!
1. \( e^{t}(y-t) d t+\left(1+e^{t}\right) d y=0 \) (4 puntos) 2. \( \left[2 x+y^{2}-\cos (x+y)\right] d x+\left[2 x y-\cos (x+y)-e^{y}\right] d y=0 \) (4 pts) 3. \( \cos (x+y) d y=\sin (x+y) d x \) (42 answers -
2 answers
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Given \( f(x, y)=2 x^{2} y-7 x y^{2} \) \[ \frac{\partial^{2} f}{\partial x^{2}}= \] \[ \frac{\partial^{2} f}{\partial y^{2}}= \]2 answers -
2) Find the derivative of a) \( y=\left(x-2 x^{4}\right)^{5}(\sin 2 x) \) b) \( y=\frac{e^{\tan x}}{\sqrt{3 x^{6}-\sec \frac{1}{x}}} \) c) \( y=\frac{6 e^{x}}{\sqrt{8 x+\ln x}} \) d) \( f(x)=\cos \lef2 answers -
El modelo de bicicleta es ampliamente usado en dinámica de vehÃculos para estudiar la dinámica lateral. El modelo de bicicleta está dado por el siguiente sistema de ecuaciones diferenciales: ​â€
\( \begin{array}{l}\dot{\beta}=-\frac{c_{r}+c_{f}}{m v} \beta+\left(\frac{c_{r} l_{r}-c_{f} l_{f}}{m v^{2}}-1\right) r+\frac{c_{f}}{m v} \delta \\ \dot{r}=\frac{l_{r} c_{r}-l_{f} c_{f}}{I_{z}} \beta-\2 answers -
7. Given \( y=\left[\begin{array}{lll}3 & 1 & -2\end{array}\right] \), find the magnitude of \( y \).2 answers