# Solve the following differential equation : $(y+3x^2)\large\frac{dx}{dy}$$=x. ## 1 Answer Toolbox: • When the function occurs in the form of their products, we can differentiate them using product rule, which states that uv = uv' + vu' Step 1: (y+3x^2)\large\frac{dx}{dy}$$=x$
This can be written as
$(y+3x^2)dx=xdy$
On rearranging we can write this as
$\large\frac{xdy-ydx}{x^2}$$=3 Step 2: On integrating we get, \int\large\frac{xdy-ydx}{x^2}$$=\int 3 dx$