Question

помогите решить 4 задание​

Answer 1

$x^2\, dy+(y+2)\, dx=0\; \; ,\; \; y(1)=-1\\\\\int \frac{dy}{y+2}=-\int \frac{dx}{x^2}\\\\ln|y+2|=-\frac{x^{-1}}{-1}+C\\\\ln|y+2|=\frac{1}{x}+C\\\\y(1)=-1:\; \; \underbrace {ln1}_{0}=1+C\; \; ,\; \; C=-1\\\\\\\boxed {ln|y+2|=\frac{1}{x}-1}$

$|y+2|=e^{\frac{1}{x}-1}\\\\|y+2|=e^{\frac{1-x}{x}}\\\\y+2=\pm e^{\frac{1-x}{x}}\\\\\boxed {y_{chastn.}=\pm e^{\frac{1-x}{x}}-2}$