We see (dˆ2*y) / (dxˆ2) = 18x-8, this just means the second derivative of some function y is 18x-8, so here goes.

(dˆ2*y) / (dxˆ2) = 18x-8

=> dy/dx = 9x^2 - 8x + C ..................integrated both sides to reverse the derivative

dy/dx gives equation for the slope, which is 9 when x = 1

=> 9 = 9(1)^2 - 8(1) + C

=> C = 8

So dy/dx = 9x^2 + 8x + 8

=> y = 3x^3 - 4x^2 + 8x + D .................again integrated both sides

we have the point (1,-1), so y=-1, when x = 1

=> -1 = 3(1)^3 - 4(1)^2 + 8(1) + D

=> D = -8

So the curve is y = 3x^3 - 4x^2 + 8x - 8