What is the solution for (dy)/(dx)+(2y)/(x+4)=(x+4)^7 ?

The solution for (dy)/(dx)+(2y)/(x+4)=(x+4)^7 is

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(dy)/(dx)+(2y)/(x+4)=(x+4)^7

\frac{d y}{d x} + \frac{2 y}{x + 4} = (x + 4)^{7}

y = \frac{x ^{10}}{10 ( x ^{2} + 8 x + 16 )} + \frac{4 x ^{9}}{x ^{2} + 8 x + 16} + \frac{72 x ^{8}}{x ^{2} + 8 x + 16} + \frac{768 x ^{7}}{x ^{2} + 8 x + 16} + \frac{5376 x ^{6}}{x ^{2} + 8 x + 16} + \frac{129024 x ^{5}}{5 ( x ^{2} + 8 x + 16 )} + \frac{86016 x ^{4}}{x ^{2} + 8 x + 16} + \frac{196608 x ^{3}}{x ^{2} + 8 x + 16} + \frac{294912 x ^{2}}{x ^{2} + 8 x + 16} + \frac{262144 x}{x ^{2} + 8 x + 16} + \frac{c _{1}}{x ^{2} + 8 x + 16}

Solution steps

\frac{d y}{d x} + \frac{2 y}{x + 4} = (x + 4)^{7}

Solve linear ODE:

y = \frac{x ^{10}}{10 ( x ^{2} + 8 x + 16 )} + \frac{4 x ^{9}}{x ^{2} + 8 x + 16} + \frac{72 x ^{8}}{x ^{2} + 8 x + 16} + \frac{768 x ^{7}}{x ^{2} + 8 x + 16} + \frac{5376 x ^{6}}{x ^{2} + 8 x + 16} + \frac{129024 x ^{5}}{5 ( x ^{2} + 8 x + 16 )} + \frac{86016 x ^{4}}{x ^{2} + 8 x + 16} + \frac{196608 x ^{3}}{x ^{2} + 8 x + 16} + \frac{294912 x ^{2}}{x ^{2} + 8 x + 16} + \frac{262144 x}{x ^{2} + 8 x + 16} + \frac{c _{1}}{x ^{2} + 8 x + 16}

y = \frac{x ^{10}}{10 ( x ^{2} + 8 x + 16 )} + \frac{4 x ^{9}}{x ^{2} + 8 x + 16} + \frac{72 x ^{8}}{x ^{2} + 8 x + 16} + \frac{768 x ^{7}}{x ^{2} + 8 x + 16} + \frac{5376 x ^{6}}{x ^{2} + 8 x + 16} + \frac{129024 x ^{5}}{5 ( x ^{2} + 8 x + 16 )} + \frac{86016 x ^{4}}{x ^{2} + 8 x + 16} + \frac{196608 x ^{3}}{x ^{2} + 8 x + 16} + \frac{294912 x ^{2}}{x ^{2} + 8 x + 16} + \frac{262144 x}{x ^{2} + 8 x + 16} + \frac{c _{1}}{x ^{2} + 8 x + 16}

\int \frac{x ^{4}}{x ^{2} + 4 x + 4} d x

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What is the solution for (dy)/(dx)+(2y)/(x+4)=(x+4)^7 ?
The solution for (dy)/(dx)+(2y)/(x+4)=(x+4)^7 is