Question

y' = 3y + 1;
yy' = 2x
Решить эти интегралы

Answer 1

$1)\; \; y'=3y+1\\\\ \frac{dy}{dx} =3y+1\\\\\int \frac{dy}{3y+1} =\int dx\\\\\frac{1}{3}\cdot ln|3y+1|=x+C\\\\2)\; \; yy'=2x\\\\ y\cdot \frac{dy}{dx}= 2x\\\\\int y\cdot dy=\int 2x\cdot dx\\\\ \frac{y^2}{2}=x^2+C$