What is the solution to the differential equation dy/dx = 2x-1/3 with the initial condition y ( 2 ) = − 2 ?

Answer 1

integrate 2x-1/3

y = x^2 -x/3 + c

plug in the point (2,-2)

y(2) = 2^2 -2/3 + c = -2

solve for c

c =-2 -4+2/3 = -4/3

y = x^2 -x/3 -4/3