Solve the initial value problem 2yy′+6=y2+6x with y(0)=9. to solve this, we should use the substitution u= y^2+6x (formulas) with this substitution, y= sqrt(u-6x) (formulas) y′= (formulas) enter derivatives using prime notation (e. g., you would enter y′ for dydx). after the substitution from the previous part, we obtain the following linear differential equation in x, u,u′. (equations) the solution to the original initial value problem is described by the following equation in x, y. (equations)