What is the solution for (dy)/(dx)=-4^{-2}-y^{-1}+y^{-1}+y ?

The solution for (dy)/(dx)=-4^{-2}-y^{-1}+y^{-1}+y is y=-(e^{x+c_{1}})/(16)+1/16

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(dy)/(dx)=-4^{-2}-y^{-1}+y^{-1}+y

\frac{d y}{d x} = - 4^{- 2} - y^{- 1} + y^{- 1} + y

y = - \frac{e ^{x + c_{1}}}{16} + \frac{1}{16}

Solution steps

\frac{d y}{d x} = - 4^{- 2} - y^{- 1} + y^{- 1} + y

Solve separable ODE:

y = - \frac{e ^{x + c_{1}}}{16} + \frac{1}{16}

y = - \frac{e ^{x + c_{1}}}{16} + \frac{1}{16}

y^{^{''}} - \frac{3}{x} y^{^{'}} - \frac{12}{x ^{2}} y = 4 x^{2}

\int \frac{1}{x 36 x ^{2} - 1} d x

\int 6 x^{2} e^{6 x} d x

y = x^{3} + x^{2} - 6 x, y = 6 x

e^{(3 t)} (4 cos (3 t) - \frac{10}{3} sin (3 t))

What is the solution for (dy)/(dx)=-4^{-2}-y^{-1}+y^{-1}+y ?
The solution for (dy)/(dx)=-4^{-2}-y^{-1}+y^{-1}+y is y=-(e^{x+c_{1}})/(16)+1/16