Question

x dy/dx+3x+y=0

Answer 1

Given equation is $x\frac{dy}{dx}+3x+y = 0$

Equation can be written as $\frac{dy}{dx} + \frac{y}{x} = - 3$

Integrating factor is $e^{\int \frac{dx}{x} } = x$

Then multiplying by the integrating factor and integrating,

$xy = \int -3xdx$

$xy = -\frac{3x^2}{2}+C$