Advanced Math Archive: Questions from February 03, 2023
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Please solve the given DE
1. \( \left(D^{8}+D^{6}-16 D^{4}-64 D^{2}\right) y=0 \) 2. \( \left(D^{2}-4 D+5\right) y=0 \) when \( x=0, y=1, y^{\prime}=0 \) 3. \( \left(D^{3}-2 D^{2}+5 D\right) y=x^{2}-\sin (x) \) 4. \( \left(D^{2 answers -
2 answers
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I just need a detailed solution to problem 10, please! Thank you so much!
8. \( x \log x d y+\sqrt{1+y^{2}} d x=0 \). 10. \( x \cos y d x+x^{2} \sin y d y=a^{2} \sin y d y \). 11. \( \frac{d r}{d \theta}=r \tan \theta \). 12. \( (x-1) \cos y d y=2 x \sin y d x \). 13. \( y^2 answers -
match, the right side with the left side
1. \( L\left\{e^{-7 t}\right\}= \) 2. \( L\{\sin 2 t\}= \) 3. \( L\left\{t^{5}\right\}= \) \( \frac{\frac{1}{2}}{s^{2}-\frac{1}{4}} \) \( \frac{2}{s^{2}+4} \) \( \frac{\sqrt{3}}{s^{2}+3} \) \( \frac{12 answers -
Laplace tranform
Problema: Discuta como usted determina la transformada de Laplace de la siguiente funci贸n: \[ f(t)=\left\{\begin{array}{c} 2,0 \leq t2 answers -
2 answers
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2 answers
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Encuentre \( L\left\{e^{2 t-1}\right\} \) \[ \frac{e}{s-2} \] \[ \frac{1}{s-(2 t-1)} \] \[ \frac{1}{e(s-2)} \] \[ \frac{2}{s-e} \] Ninguna de las anteriores2 answers -
Encuentre \( L\{4 \sin t \) cost \( \} \). Hint: use una identidad \[ \frac{2}{s^{2}+2} \] \[ \frac{4}{s^{2}+4} \] \[ \frac{2 s}{s^{2}+4} \] \[ \frac{2}{s^{2}+4} \] ninguna de las anteriores2 answers -
What are the equilibrium solutions of the equation below? \[ \frac{d y}{d t}=\frac{\left(y^{2}-9\right)(t-4)}{(y+7)} \] \[ \begin{array}{l} y=3 \\ y=3, y=-3 \\ y=3, y=-3, t=4 \\ y=3, y=-3, y=-7 \\ y=32 answers -
(Click on a graph to enlarge it) \[ y=f(x+2) \] \[ y=-f(x) \] \[ y=f(x)-2 \] \[ y=f(-x) \] \[ y=f(x-2) \] (Click on a graph to enlarge it) \[ y=f(x-1) \] \[ y=f(x-5) \] \[ y=f(-x) \] \[ y=f(x+3) \] \2 answers -
Solve the system \[ \left\{\begin{aligned} 4 x_{1}-3 x_{2}+2 x_{3}+4 x_{4}= & 2 \\ -x_{1}+x_{2}+2 x_{3}+2 x_{4}= & 1 \\ 3 x_{1}-2 x_{2}+4 x_{3}+6 x_{4}= & 3 \\ -3 x_{1}+3 x_{2}+6 x_{3}+6 x_{4}= & 3 \e2 answers -
Encuentre \( L\left\{e^{2 t-1}\right\} \) \( \frac{e}{s-2} \) \[ \frac{1}{s-(2 t-1)} \] \[ \frac{1}{e(s-2)} \] \[ \frac{2}{s-\theta} \] Ninguna de las anteriores2 answers -
\( \left(\sum_{k=0}^{\infty}\left(\frac{99}{100}\right)^{k} \times\left(\cos ^{2} x+\sin ^{2} x\right)\right)-\lim _{x \rightarrow \infty} \frac{324 x^{3}-3 x^{2}-10 x}{4 x^{3}-9 x^{2}+3 x} \)2 answers -
Solve using the method of characteristic polynomial \[ y^{\prime \prime \prime}-2 y^{\prime \prime}-y^{\prime}+2 y=0, y(0)=0, y^{\prime}(0)=1, y^{\prime \prime}(0)=1 \]2 answers -
2 answers
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1 answer
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2 answers
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Find the following using and identity
Encuentre \( L\{4 \operatorname{sintcost}\} \). Hint. use una identidad2 answers -
1) Selecciono 2 de las siguientes funciones: a) \( f(x)=-\sqrt{9-x}+1 \) b) \( x(x)=(x-1)^{3}-1 \) c) \( h(x)=-(x-2)^{2}+2 \) usndin mitoriormeche2 answers -
1. Halle la estructura algebraica de la funci贸n descrita por ser la funci贸n racional reflejada con respecto al oje de y. trasladada 4 unidades a la izquierda sobre el eje de \( x \) y que sube dos u2 answers -
Find extremals for the following functional. \[ \begin{array}{c} J(y)=\int_{0}^{1}\left(y y^{\prime}+\left(y^{\prime \prime}\right)^{2}\right) d x \\ y(0)=0, y^{\prime}(0)=1, y(1)=2, y^{\prime}(1)=4 \2 answers -
2 answers