What is the solution for (dy)/(dx)+y=y^{-1/2} ?

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

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(dy)/(dx)+y=y^{-1/2}

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

y = (- e^{- \frac{3 x + c _{1}}{2}} + 1)^{\frac{2}{3}}

Solution steps

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

Solve separable ODE:

y = (- e^{- \frac{3 x + c _{1}}{2}} + 1)^{\frac{2}{3}}

y = (- e^{- \frac{3 x + c _{1}}{2}} + 1)^{\frac{2}{3}}

f (x) (x + 1) = f^{^{'}} (x)

\frac{d y}{d x} = \frac{( x y + 5 x - y - 5 )}{x y - 2 x + 6 y - 12}

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

\frac{d y}{d x} = \frac{7 x y}{( ln ( y ) ) ^{10}}

\frac{d y}{d x} + \frac{y}{6} = 0

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