Solve the differential equation: dy/dx = 6x^2 + 4x + 9

dy/dx = 6x² + 4x + 9

dy = (6x² + 4x + 9) dx 

integrating gives:

y= (6x³/3) + (4x²/2) + 9x + c

y= 2x³ + 2x² + 9x + c

If given boundary conditions of y(0)=0 then 

0 = 2(0)³ + 2(0)² +9(0) +c 

therefore c=0 

so y= 2x³ + 2x² + 9x