Solve the initial value problem yy′+x=x2+y2√ with y(1)=8‾√. to solve this, we should use the substitution u= x^2+y^2 (formulas) u′= 2x+2yy' (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′.