What is the solution for (dy)/(dx)=-2y^{3/2}tan(x) ?

The solution for (dy)/(dx)=-2y^{3/2}tan(x) is y= 4/(4ln^2(cos(x))+4c_{1)ln(cos(x))+c_{1}^2}

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(dy)/(dx)=-2y^{3/2}tan(x)

\frac{d y}{d x} = - 2 y^{\frac{3}{2}} tan (x)

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

Solution steps

\frac{d y}{d x} = - 2 y^{\frac{3}{2}} tan (x)

Solve separable ODE:

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

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

\frac{d y}{d t} = - 0.2 y

P^{^{'}} = 0.2 P

x^{^{'}} = k x

\frac{d x}{d y} y = 9 x^{2}

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

What is the solution for (dy)/(dx)=-2y^{3/2}tan(x) ?
The solution for (dy)/(dx)=-2y^{3/2}tan(x) is y= 4/(4ln^2(cos(x))+4c_{1)ln(cos(x))+c_{1}^2}