## Calculus 10th Edition

The particular solution that satisfies the intial condition is $y=(28-x^{\frac{3}{2}} )^{\frac{2}{3}}$
Start by integrating the differential equation using separation of variables $\sqrt x +\sqrt y y' = 0$ $\int \sqrt y dy = \int - \sqrt x dx$ $\frac{2}{3} y^{\frac{3}{2}} = -\frac{2}{3} x^{\frac{3}{2}} +C$ Let $\frac{3}{2} C = C'$ $y^{\frac{3}{2}} = - x^{\frac{3}{2}} +C'$ Use the initial condition to solve for C' $(\sqrt 9)^3 = -(\sqrt 1)^3 +C'$ Simplify $C'= 28$ Substitute the C' value back into the general solution $y^{\frac{3}{2} }= -x^{\frac{3}{2}} +28$ $y=(28-x^{\frac{3}{2}} )^{\frac{2}{3}}$