ABTo solve the differential equation y′′=√(2x-y+1)+2, we can use the substitution u = 2x-y+1 and integrate both sides of the resulting equation.
To solve the differential equation y′′=√(2x-y+1)+2, we can use the substitution u = 2x-y+1. Differentiating both sides of this equation with respect to x gives du/dx = -2y' + 2. Now, substitute the value of y' into the original equation to get y'' = √u + 2. So, the equation becomes -2y' + 2 = √u + 2. Rearranging the terms, we get y' = -√u.
Integrating both sides of this equation gives us y = -∫√u dx.
Therefore, the solution to the differential equation y′′=√(2x-y+1)+2 is y = -∫√u dx, where u = 2x-y+1.