Other Math Archive: Questions from February 16, 2023
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Solve the differential equations: (ONLy simple Answer) 1) \( \frac{d y}{d x}=\frac{1}{x \cos y+\sin 2 y^{\prime}} \) 3) \( \frac{d y}{d x}+2 x y=y^{2} e^{3} \) 4) \( \left(x^{3}+y^{3}\right) d x-3 x y2 answers -
2 answers
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\[ \begin{array}{l} \text { Let } U=\{q, i, s, t, u, v, w, x, y, z\} \text {, } \\ A=\{q, s, u, w, y\}, \\ B=\{q, s, y, z\}, \text { and } \\ C=\{v, w, x, y, z\} \end{array} \] Determine the elements2 answers -
linear differential equations
9. \( \frac{d y}{d x}-y=e^{2 x} \), 10. \( \frac{d y}{d x}+y=e^{2 x} \), 11. \( x y^{\prime}+y=x^{3} \), 12. \( y^{\prime}+a y=b \), 13. \( \frac{d x}{d y}+2 y x=e^{-y^{2}} \), 14. \( \frac{d r}{d \th2 answers -
number 4
In Problems 1-8, find a general solution to the differential equation using the method of variation of parameters. 1. \( y^{\prime \prime}+y=\sec t \) 2. \( y^{\prime \prime}+4 y=\tan 2 t \) 3. \( y^{2 answers -
answer 21
In Problems 9-26, find a particular solution to the differential equation. 9. \( y^{\prime \prime}+2 y^{\prime}-y=10 \) 10. \( y^{\prime \prime}+3 y=-9 \) 11. \( y^{\prime \prime}(x)+y(x)=2^{x} \) 12.3 answers -
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In Problems 19-21, solve the given initial value problem. 19. \( y^{\prime \prime \prime}-y^{\prime \prime}-4 y^{\prime}+4 y=0 \); \[ y(0)=-4, \quad y^{\prime}(0)=-1, \quad y^{\prime \prime}(0)=-19 \]2 answers -
Resolver este problema de valor inicial usando el método de solución de Reducción a Separable, según discutido en clase. Escribir la respuesta en la forma \( y=f(x) \) completamente simplificada.2 answers -
2]- Find the divergence: a) \( \vec{v}=\frac{4 y}{x^{2}} i+\sin (y) j+3 k \) b) \( \vec{v}=e^{x} i+\ln (\mathrm{xy}) j+e^{x y z} k \)2 answers