Question

$\frac{dy}{dx} = {y}^{2} x$
y(5)=2помогите решить

Answer 1

$\dfrac{dy}{dx}=y^2x\medskip\\\dfrac{1}{y^2}dy=xdx\medskip\\\displaystyle\int y^{-2}dy=\int x dx\medskip\\-y^{-1}=\dfrac{x^2}{2}+C_1\medskip\\y^{-1}=-\dfrac{x^2+2C_2}{2}\medskip\\y=-\dfrac{2}{x^2+C}\medskip\\y(5)=-\dfrac{2}{25+C}=2\Rightarrow 50+2C=-2\Rightarrow C=-26$

Ответ. $y=-\dfrac{2}{x^2-26}$