Mechanical Engineering Archive: Questions from April 07, 2023
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suelve \( y \frac{d x}{d y}=x+4 y e^{-2 x y} \) \[ \begin{array}{l} \frac{1}{2} e^{2 x y}=\ln \mid y+c \\ 2 e^{2 x y}=8 \ln |y|+c \\ e^{2 x y}=8 \ln \mid y+c \\ 4 e^{2 x y}=2 \ln |y|+c \end{array} \]2 answers -
suelve \( y \frac{d x}{d y}=x+4 y e^{-2 x y} \) \[ \frac{1}{2} e^{2 x y}=\ln \mid y+c \] \( 2 e^{2 x y}=8 \ln |y|+c \) \[ e^{2 x y}=8 \ln \mid y+c \] \[ 4 e^{2 x y}=2 \ln |y|+c \] Ninguna de las anter2 answers -
suelve \( \left(y+x \cot \frac{y}{x}\right) d x-x d y=0 \) \( \ln \cos \frac{y}{x}|=\ln | x \mid+c \) \[ x \cos \frac{y}{x}=c \] \[ \ln |x|=\sec ^{2}\left(\frac{y}{x}\right)+c \] Ninguna de las anteri2 answers -
esuelva \( 2 x^{2} y d x=\left(3 x^{3}+y^{3}\right) d y \) \[ y^{9}=c\left(x^{3}+y^{3}\right)^{2} \] \[ \frac{c}{y^{9}}=\left(x^{3}+y^{3}\right)^{2} \] \[ \frac{2}{3} \ln \left(x^{3}+y^{3}\right)^{2}=2 answers -
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