Advanced Math Archive: Questions from June 09, 2023
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Q6) \( 4 x^{2}-24 x-25 y^{2}+250 y-489=0 \). Find the equations of the asymptotes? A) \( y=3 x+5 \) B) \( y-5=\mp \frac{2}{5}(x-3) \) C) \( y-3=\mp \frac{2}{5}(x-5) \) D) \( y+1=\mp \frac{1}{3}(x+2) \2 answers -
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The solution of the boundary value problem: \( y^{\prime \prime}+4 y=0, y(0)=1, y^{\prime}(\pi / 4)=0 \) is (i) \( y=\sin 2 x \) (ii) \( y=\cos 2 x \) (iii) \( y=\cos (4 x) \) (iv) \( y=\sin (4 x) \)2 answers -
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Solve the differential equations below: i. \( (2 x y-3) d x+\left(x^{2}+4 y\right) d y=0, y(1)=0 \). ii. \( (y+2) d x+y(x+4) d y=0, y(-3)=-1 \). iii. \( \left(3 x^{2} y^{2}-y^{3}+2 x\right) d x+\left(0 answers -
Using variation of parameters, find the general solution of the differential equations below: i. \( y^{\prime \prime}+y=\tan x \) ii. \( \left(x^{2}+1\right) y^{\prime \prime}-2 x y^{\prime}+2 y=6\lef2 answers -
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4. Las siguientes preguntas giran alrededor \( y^{\prime}+\tan (x) y=\cos ^{2}(x) \) a. Determinar un factor integrante \( y \) hallar la solución general de esta edo No-homogénea. b. Indicar claram0 answers -
3. Recordemos que solo trabajamos solo con funciones reales \( f: \mathbb{R} \rightarrow \mathbb{R} \). Hallar si existe (o explicar por qué no existe) una ecuación diferencial homogénea que tenga2 answers -
Solve the given initial-value problem. y(x) = y" - y = cosh(x), y(0) = 8, y'(0) = 14
Solve the given initial-value problem. \[ y^{\prime \prime}-y=\cosh (x), y(0)=8, y^{\prime}(0)=14 \] \[ y(x)= \]2 answers -
find the determinant
Problem \[ \left[\begin{array}{ccc} \cos x \cos y & \cos x \sin y & -\sin x \\ -\sin y & \cos y & 0 \\ \sin x \cos y & \sin x \sin y & \cos x \end{array}\right] \]2 answers -
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y tasa de satial. \( g(n)=\operatorname{sen}(x) \) y \( h(x)=\tan (x) \) \[ \begin{array}{l} y^{n+}-k y^{\prime \prime}+k^{3} y^{\prime}-k^{3} y+9 \\ y(0)=y^{\prime}(0)=0 ; y^{\prime}(0)=1 \end{array}0 answers -
\( X(\omega)=\left\{\sin (7 \omega) \delta\left(\omega+\frac{3 \pi}{2}\right)+\cos (2 \omega) \delta\left(\omega-\frac{3 \pi}{2}\right)\right\} e^{-j \omega}, x(t)=? \)2 answers -
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