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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

(3 x + 8) (y^{2} + 4) d x - 4 y (x^{2} + 5 x + 6) d y = 0

\frac{d y}{d x} = \frac{y ln ( x )}{x}

y^{^{'}} = x y^{3} (1 + x^{2})^{- \frac{1}{2}}, y (0) = 1

y^{^{'}} + ln (x) y = 3 ln (x)

x^{2} y^{^{'}} + y = - 2

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