Other Math Archive: Questions from November 18, 2022
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(40 points) Solve the initial value problem \[ y^{\prime \prime}+5 x y^{\prime}-20 y=0, y(0)=1, y^{\prime}(0)=0 \text {. } \] \[ y= \]2 answers -
\( y^{\prime \prime}-3 y^{\prime}-10 y=x^{2}+e^{3 x} \) \( y^{\prime \prime}+10 y^{\prime}+25 y=20 \cos 2 x \) \( y^{\prime \prime}+y=\tan x \)1 answer -
Solve the IVP: (a) \( y^{\prime \prime}-4 y=x+e^{-3 x}, y(0)=1, y^{\prime}(0)=2 \) (b) \( y^{\prime \prime}+5 y^{\prime}-6 y=10 e^{2 x}, y(1)=2, y^{\prime}(1)=-1 \)2 answers -
171. In each part, determine whether \( T \) is a matrix transformation. (a) \( T(x, y, z)=(0,0) \) (b) \( T(x, y, z, w)=(1,-1) \) (c) \( T(x, y, z)=(x-y+z, 0) \) (d) \( T(x, y, z)=(x, y z, x+y+z) \)2 answers -
Solve the initial value problem \[ \begin{array}{c} y^{\prime \prime}-y^{\prime}+2 y=3 e^{-x}-10 \cos 3 x \\ y(0)=1, y^{\prime}(0)=2 \end{array} \]2 answers -
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2 answers
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considering the initial value problem y′′−4y′+5y=e 0.2x,y(0)=1,y′(0)=0.3. complete the table using Euler's method x y(x) 0 0.3 0.6 0.9 1.2
(1 point) Cosiderando el problema de valores iniciales \[ y^{\prime \prime}-4 y^{\prime}+5 y=e^{0.2 x}, \quad y(0)=1, \quad y^{\prime}(0)=0.3 . \] completa la tabla usando el método de Euler2 answers -
Using Laplace Transforms find the particular solution of the differential equation d two Y dt2 + dy dt − 2y = 30e −t sin(t) subject to y(0) = 30 y y ′ (0) = 0.
3. Usando Transformadas de Laplace hallar la solución particular de la ecuación diferencial \( \frac{d^{2} y}{d t^{2}}+\frac{d y}{d t}-2 y= \) \( 30 e^{-t} \sin (t) \) sujeta a \( y(0)=30 \) y \( y^2 answers -
In Exercises 7-12, determine the matrix for the given transformation. 8. \( (x, y, z)^{\prime}=(x \cos \theta-z \sin \theta, y, x \sin \theta+z \cos \theta) \) 10. \( (x, y, z)^{\prime}=(x,-z, y) \) 12 answers