Question

помогите решить 2 задание​

Answer 1

$(1+x^2)\, dy-2x\, (y+3)\, dx=0\; \; ,\; \; \; y(0)=-1\\\\\int \frac{dy}{y+3}=\int \frac{2x\, dx}{1+x^2}\\\\ln|y+3|=ln|1+x^2|+ln|C|\\\\y+3=C(1+x^2)\\\\y_{obshee}=C(1+x^2)-3\\\\y(0)=-1:\; \; -1=C(1+0^2)-3\; \; ,\; \; C=2\\\\\underline {y_{chastnoe}=2\, (1+x^2)-3}$