What is the solution for y^'=-sqrt(xy),y(0)=1 ?

The solution for y^'=-sqrt(xy),y(0)=1 is y=(x^3)/9-(2x^{3/2})/3+1

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y^'=-sqrt(xy),y(0)=1

y^{^{'}} = - x y, y (0) = 1

y = \frac{x ^{3}}{9} - \frac{2 x ^{\frac{3}{2}}}{3} + 1

Solution steps

y^{'} (x) = - x y

Solve separable ODE:

y = \frac{x ^{3}}{9} - \frac{2 x ^{\frac{3}{2}}}{3} + 1

y = \frac{x ^{3}}{9} - \frac{2 x ^{\frac{3}{2}}}{3} + 1

x (x - 1) \frac{d y}{d x} = y

\frac{d y}{d x} = (\frac{y}{20000}) x

(sin (x) sin (y)) d y = (cosh (x) cos (y)) d x

\frac{d x}{d t} = 60 - \frac{1}{100} x

\frac{d P}{d t} P = (5000 (2)^{- \frac{t}{10}})

What is the solution for y^'=-sqrt(xy),y(0)=1 ?
The solution for y^'=-sqrt(xy),y(0)=1 is y=(x^3)/9-(2x^{3/2})/3+1