$$ 2y'+3 \frac yx=0 $$
$$ 2\frac{dy}{dx}=-3 \frac yx $$
$$ \frac 2y \quad \frac{dy}{dx}=-\frac3 x $$
$$\int \quad \frac 2y \quad \frac{dy}{dx}\quad dx =-\int \quad \frac3 x \quad dx $$
$$\int \quad \frac 2y \quad dy =-\int \quad \frac3 x \quad dx $$
$$2 \cdot \ln \mid y \mid =-3 \cdot \ln \mid x \mid +C_1$$
$$ \ln \mid y \mid =-\frac 32 \cdot \ln \mid x \mid +C_1$$
$$ \ln \mid y \mid = \ln \mid x^{-\frac 32} \mid +C_1$$
$$ e^{ \ln \mid y \mid } = e^{ \ln \mid x^{-\frac 32} \mid +C_1}$$
$$ y = x^{-\frac 32} \cdot C_2$$
