Advanced Math Archive: Questions from February 08, 2023
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\( \begin{array}{l}y^{\prime \prime}-y^{\prime}=\cos t+1, \quad y(0)=y^{\prime}(0)=0 \\ y=-1+\frac{3}{2} e^{t}-\frac{1}{2}(\sin t+\cos t)-t\end{array} \)2 answers -
4. Solve the IVP: \( y^{\prime \prime}+4 y^{\prime}+3 y=t, \mathrm{y}(0)=1, \mathrm{y}^{\prime}(0)=2 \). 5. Solve the IVP: \( 4 y^{\prime \prime}-y^{\prime}=x e^{x / 2}, \quad y(0)=1, \quad y^{\prime}2 answers -
2 answers
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1. Solve the following separable equation (a) \( \frac{d y}{d x}-\frac{1-x^{2}}{y^{2}}=0 \) (b) \( \left(1+e^{x}\right) y y^{\prime}=e^{x} \) (c) \( \frac{d y}{d x}-y(2+\sin x)=0 \) (d) \( \frac{1}{y}2 answers -
1 answer
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Find \( x \) and \( y \). \[ \left[\begin{array}{rr} -7 & x \\ y & 2 \end{array}\right]=\left[\begin{array}{rr} -7 & 15 \\ 14 & 2 \end{array}\right] \]2 answers -
(1 point) Find the partial derivatives of the function \[ f(x, y)=x y e^{3 y} \] \[ \begin{array}{l} f_{x}(x, y)= \\ f_{y}(x, y)= \\ f_{x y}(x, y)= \end{array} \]2 answers -
(1 point) Calculate all four second-order partial derivatives of \( f(x, y)=(3 x+5 y) e^{y} \). \[ f_{x x}(x, y)= \] \[ f_{x y}(x, y)= \] \[ f_{y x}(x, y)= \] \[ f_{y y}(x, y) \]2 answers -
2 answers
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Find the area of the trapezoid. A. \( 24 \mathrm{mi}^{2} \) B. \( 16 m i^{2} \) C. \( 400 m i^{2} \) D. \( 20 m i^{2} \)2 answers -
2 answers
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Problem: Discuss how you determine the Laplace transform of the following function:
Problema: Discuta como usted determina la transformada de Laplace de la siguiente función: \[ f(t)=\left\{\begin{array}{c} 2,0 \leq t2 answers -
Find the following inverse Laplace transforms:
Hallar las siguientes transformadas de Laplace inversas: 1. \( L^{-1}\left\{\frac{1}{s^{4}}\right\} \) 2. \( L^{-1}\left\{\frac{1}{s^{2}}-\frac{48}{s^{5}}\right\} \) 3. \( L^{-1}\left\{\frac{1}{4 s+1}2 answers -
Resolver el problema de valores iniciales dado por la ecuación diferencial: Con condiciones iniciales: \[ y(0)=0, \quad y^{\prime}(0)=\frac{1}{2} \]2 answers -
Resolver el problema de valores iniciales dado por la ecuación diferencial: \[ y^{\prime \prime}-3 y^{\prime}+2 y=2 e^{2 t} \] Con condiciones iniciales: \[ y(0)=0, \quad y^{\prime}(0)=4 \]2 answers -
Solve and show procedure.
Problema: Explique cómo hallar \[ L^{-1}\left\{\frac{1}{s^{2}(s+1)}\right\} \]2 answers -
need help with 7(b)
7. Classify each equation as linear or nonlinear: (a) \( y^{\prime}+e^{x} y=4 \) (b) \( y y^{\prime}=x+y \) (c) \( e^{x} y^{\prime}=x-2 y \) (d) \( y^{\prime}-\exp y=\sin x \) (e) \( y^{\prime \prime}2 answers -
need help with 7(d)
7. Classify each equation as linear or nonlinear: (a) \( y^{\prime}+e^{x} y=4 \) (b) \( y y^{\prime}=x+y \) (c) \( e^{x} y^{\prime}=x-2 y \) (d) \( y^{\prime}-\exp y=\sin x \) (e) \( y^{\prime \prime}2 answers -
need help with 7(g) thank you!
7. Classify each equation as linear or nonlinear: (a) \( y^{\prime}+e^{x} y=4 \) (b) \( y y^{\prime}=x+y \) (c) \( e^{x} y^{\prime}=x-2 y \) (d) \( y^{\prime}-\exp y=\sin x \) (e) \( y^{\prime \prime}1 answer -
ecucaciones 11.1 assesment
Hallar las siguientes transformadas de Laplace inversas: 1. \( L^{-1}\left\{\frac{1}{s^{4}}\right\} \) 2. \( L^{-1}\left\{\frac{1}{s^{2}}-\frac{48}{s^{5}}\right\} \) 3. \( L^{-1}\left\{\frac{1}{4 s+1}2 answers -
ecuaciones 11.1 asigment
\[ \begin{array}{l} \text { 1. } y^{\prime}+6 t=e^{4 t}, y(0)=2 \\ 2 y^{\prime \prime}+6 y^{\prime}+4 y=0, y(0)=1, y^{\prime}(0)=0 \\ \text { 3. } y^{\prime}+t=e^{5 t}, y(0)=1 \\ \text { 4. } y^{\prim2 answers -
calculo 8.1 assigment
1. Utilice la integral doble para comprobar que los momentos de inercia en la región con respecto a los ejes son los que se ilustran en la figura. Luego calcule los radios de giro con respecto a cada2 answers -
Solve the given initial value problem. \[ y^{\prime \prime}+6 y^{\prime}+34 y=0 ; \quad y(0)=3, \quad y^{\prime}(0)=-7 \] \[ y(t)=3 e^{-3 t} \cos 5 t+\frac{1}{2} e^{-3 t} \sin 5 t \]2 answers -
the IVP: \( 4 y^{\prime \prime}-y^{\prime}=x e^{x / 2}, \quad y(0)=1, \quad y^{\prime}(0)=0 \) \[ 4 y^{\prime \prime}+36 y=\csc (3 x) \] \[ y=y_{c}+y_{p}=c_{1} \cos (3 x)+c_{2} \sin (3 x)-\frac{1}{12}2 answers -
2 answers
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2 answers
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For the next fourteen questions, justify each step in the following proof seque of \( (\forall x)(\forall y)[(P(x) \wedge S(x, y)) \rightarrow Q(y)] \wedge(\exists x) B(x) \wedge(\forall x)(B(x) \righ2 answers -
\( \begin{array}{l}4 y^{\prime \prime}+36 y=\csc (3 x) \\ y=y_{c}+y_{p}=c_{1} \cos (3 x)+c_{2} \sin (3 x)-\frac{1}{12} x \cos (3 x)+\frac{1}{36} \sin (3 x) \ln |\sin (3 x)| \text {. }\end{array} \)2 answers -
Solve the following IVP: \[ y^{\prime \prime}-2 y^{\prime}+y=\frac{e^{t}}{t^{2}+1} \quad y(0)=5 \quad y^{\prime}(0)=-1 \]2 answers