What is the solution for (dy)/(dx)=2xsqrt(36-y^2) ?

The solution for (dy)/(dx)=2xsqrt(36-y^2) is y=6sin(x^2+c_{1})

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(dy)/(dx)=2xsqrt(36-y^2)

\frac{d y}{d x} = 2 x 36 - y^{2}

y = 6 sin (x^{2} + c_{1})

Solution steps

\frac{d y}{d x} = 2 x 36 - y^{2}

Solve separable ODE:

y = 6 sin (x^{2} + c_{1})

y = 6 sin (x^{2} + c_{1})

\frac{d y}{d x} = \frac{1}{7} (y)^{\frac{1}{2}} (cos (y^{\frac{1}{2}}))^{2}

y^{^{'}} = \frac{y ^{4}}{x ^{6}}, y (1) = 3

x y^{^{'}} + 2 y = 1

x \cdot \frac{d x}{d y} = 4 y

\frac{d x}{d y} = 4 x^{3} y - 6 x^{2} y

What is the solution for (dy)/(dx)=2xsqrt(36-y^2) ?
The solution for (dy)/(dx)=2xsqrt(36-y^2) is y=6sin(x^2+c_{1})