What is the solution for y^'= 2/3 xsqrt(1-9y^2),y(0)=0 ?

The solution for y^'= 2/3 xsqrt(1-9y^2),y(0)=0 is y=(sin(x^2))/3

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y^'= 2/3 xsqrt(1-9y^2),y(0)=0

y^{^{'}} = \frac{2}{3} x 1 - 9 y^{2}, y (0) = 0

y = \frac{sin ( x ^{2} )}{3}

Solution steps

y^{'} (x) = \frac{2}{3} x 1 - 9 y^{2}

Solve separable ODE:

y = \frac{sin ( x ^{2} )}{3}

y = \frac{sin ( x ^{2} )}{3}

(x + 1) y^{^{'}} - 3 y = 0

y^{^{'}} = 3 x^{2} y^{2}, y (- 1) = a, y (0) = 1

\frac{d y}{d x} = \frac{x y - 4 x + y - 4}{x y - 6 x - 3 y + 18}

\frac{d y}{d x} = x^{2} (y - 2), y (0) = 4

y^{^{'}} = e^{- y}, y (0) = 0

What is the solution for y^'= 2/3 xsqrt(1-9y^2),y(0)=0 ?
The solution for y^'= 2/3 xsqrt(1-9y^2),y(0)=0 is y=(sin(x^2))/3