Example 13 Find the equation of a curve passing through the point (–2, 3), given that
the slope of the tangent to the curve at any point (x, y) is 
2x2
y Solution We know that the slope of the tangent to a curve is given by dy
dx so,
dy
dx  =
y2x2 (1)
Separating the variables, equation (1) can be written as
y2 dy = 2x dx