What is the solution for (x^2+4)(dy)/(dx)+8xy=2x ?

The solution for (x^2+4)(dy)/(dx)+8xy=2x is y=(c_{1})/(4(x^8+16x^6+96x^4+256x^2+256))+1/4

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(x^2+4)(dy)/(dx)+8xy=2x

(x^{2} + 4) \frac{d y}{d x} + 8 x y = 2 x

y = \frac{c _{1}}{4 ( x ^{8} + 16 x ^{6} + 96 x ^{4} + 256 x ^{2} + 256 )} + \frac{1}{4}

Solution steps

(x^{2} + 4) \frac{d y}{d x} + 8 x y = 2 x

Solve separable ODE:

y = \frac{c _{1}}{4 ( x ^{8} + 16 x ^{6} + 96 x ^{4} + 256 x ^{2} + 256 )} + \frac{1}{4}

y = \frac{c _{1}}{4 ( x ^{8} + 16 x ^{6} + 96 x ^{4} + 256 x ^{2} + 256 )} + \frac{1}{4}

\frac{d y}{d x} = 3 + 5 y

\frac{d y}{d x} = 7 x^{6} y

\frac{d y}{d x} = y x^{3}

\frac{d y}{d x} = \frac{y - 1}{x}

(2 x y - x + 2 y - 1) d x + (4 x^{2} y^{2} - x^{2} + 4 x y^{2} - x) d y = 0

What is the solution for (x^2+4)(dy)/(dx)+8xy=2x ?
The solution for (x^2+4)(dy)/(dx)+8xy=2x is y=(c_{1})/(4(x^8+16x^6+96x^4+256x^2+256))+1/4