Question

xdy + 2ydx = 0 если y = 2 при x = 4

Answer 1

$x\, dy+2y\, dx=0\; \; ,\; \; x\, dy=-2y\, dx\\\\\int \frac{dy}{y}=-2\int \frac{dx}{x}\\\\ln|y|=-2\, ln|x|+ln|C|\\\\y=Cx^{-2}\; \; ,\; \; y=\frac{C}{x^2}\\\\y(4)=2:\; \; 2=\frac{C}{4^2}\; \; ,\; \; C=32\\\\\boxed {y=\frac{32}{x^2} }$