Advanced Math Archive: Questions from January 22, 2023
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Solve the initial value problem. \[ \frac{d y}{d x}+x y=2 x ; y(0)=-5 \] \[ y=-7 e^{-x^{2} / 2}+2 \] \[ y=2 e^{x^{2} / 2}-7 \] \( y=2 e^{-x^{2} / 2}-7 \) \[ y=-7 e^{x^{2} / 2}+2 \]2 answers -
1. Find \( \frac{d y}{d x} \) : a. \( y=6 x^{3}+9 x+17 \) b. \( y=\ln 4 x^{4} \) c. \( y=g(x)+f(x)+h(x) k(x) \) d. \( y=\frac{4 x^{5}+8 x^{4}}{2 x^{3}} \) 2. Find \( d y \) : Note: subscripts indicate2 answers -
Ejercicio numero 2.
Determine si los siguientes vectores forman una base en \( \mathrm{R}^{3} \). 1. \( \{(1,5,3),(2,3,4),(1,9,1)\} \) 2. \( \{(0,2,6),(1,2,3),(3,4,8)\} \) Demuestre el procedimiento completo como se mues2 answers -
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Find the general solution of \( y^{\prime \prime}+3 y^{\prime}-10 y=3 x^{2} \). A. \( \quad y=C_{1} e^{2 x}+C_{2} e^{-5 x}-\frac{3}{8} x^{2}-\frac{9}{50} x-\frac{57}{500} \) B. \( y=e^{3 x}\left(C_{1}2 answers -
PLEASE SOLVE FOR GENERAL SOLUTION:
\( \left(\frac{2 x}{y}+y\right)+\left(\frac{x^{2}}{y^{2}}+3 x+\frac{1}{y^{2}}\right) y^{\prime}=0, y>0 \)2 answers