We write the equation in terms of dy/dx, <span>y'(x)=sqrt (2y(x)+18)</span> dy/dx = sqrt(2y + 18) dy/dx = sqrt(2) ( sqrt(y + 9))
Separating the variables in the equation, we will have: <span>1/sqrt(y + 9) dy= sqrt(2) dx </span>
Integrating both sides, we will obtain <span>2sqrt(y+9) = x(sqrt(2)) + c </span> <span>where c is a constant and can be determined by using the boundary condition given </span> <span>y(5)=9 : x = 5, y = 9 </span><span>sqrt(9+9) = 5/sqrt(2) + C </span>