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

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

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(dy)/(dx)=((y-1))/(x^2sqrt(4+x^2))

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

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

Solution steps

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

Solve separable ODE:

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

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

\frac{d y}{d x} - 7 e^{x - y} = 0

y + 4 y^{^{'}} + 3 y = 0

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

x sin (y) + (x^{2} + 1) cos (y) y^{^{'}} = 0

x^{2} (x d y + y d x) = 7 x d y - 7 y d x

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