What is the solution for sin(x)dx+(dy)/(sqrt(y))=0 ?

The solution for sin(x)dx+(dy)/(sqrt(y))=0 is y=(cos^2(x))/4+(c_{1}cos(x))/2+(c_{1}^2)/4

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sin(x)dx+(dy)/(sqrt(y))=0

sin (x) d x + \frac{d y}{y} = 0

y = \frac{cos ^{2} ( x )}{4} + \frac{c _{1} cos ( x )}{2} + \frac{c _{1}^{2}}{4}

Solution steps

sin (x) d x + \frac{d y}{y} = 0

Solve separable ODE:

y = \frac{cos ^{2} ( x )}{4} + \frac{c _{1} cos ( x )}{2} + \frac{c _{1}^{2}}{4}

y = \frac{cos ^{2} ( x )}{4} + \frac{c _{1} cos ( x )}{2} + \frac{c _{1}^{2}}{4}

(x^{2} - x + 1) y^{^{'}} + 4 (1 - 2 x) y = 0

x^{2} (x d y + y d x) = 4 x d y - 4 y d x

\frac{d y}{d x} = - 800 y

\frac{d y}{d x} = 14 x y

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

What is the solution for sin(x)dx+(dy)/(sqrt(y))=0 ?
The solution for sin(x)dx+(dy)/(sqrt(y))=0 is y=(cos^2(x))/4+(c_{1}cos(x))/2+(c_{1}^2)/4