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 (2)
Integrating both sides of equation (2), we get
2
∫y dy
 =
2x dx
∫
or
3
3
y  = x2 + C