What is the solution for (dy)/(dx)+(8y)/(x+2)=(x+2)^6 ?

The solution for (dy)/(dx)+(8y)/(x+2)=(x+2)^6 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)+(8y)/(x+2)=(x+2)^6

\frac{d y}{d x} + \frac{8 y}{x + 2} = (x + 2)^{6}

y = \frac{\int ( x + 2 ) ^{6} ( x ^{8} + 16 x ^{7} + 112 x ^{6} + 448 x ^{5} + 1120 x ^{4} + 1792 x ^{3} + 1792 x ^{2} + 1024 x + 256 ) d x}{x ^{8} + 16 x ^{7} + 112 x ^{6} + 448 x ^{5} + 1120 x ^{4} + 1792 x ^{3} + 1792 x ^{2} + 1024 x + 256}

Solution steps

\frac{d y}{d x} + \frac{8 y}{x + 2} = (x + 2)^{6}

Solve linear ODE:

y = \frac{\int ( x + 2 ) ^{6} ( x ^{8} + 16 x ^{7} + 112 x ^{6} + 448 x ^{5} + 1120 x ^{4} + 1792 x ^{3} + 1792 x ^{2} + 1024 x + 256 ) d x}{x ^{8} + 16 x ^{7} + 112 x ^{6} + 448 x ^{5} + 1120 x ^{4} + 1792 x ^{3} + 1792 x ^{2} + 1024 x + 256}

y = \frac{\int ( x + 2 ) ^{6} ( x ^{8} + 16 x ^{7} + 112 x ^{6} + 448 x ^{5} + 1120 x ^{4} + 1792 x ^{3} + 1792 x ^{2} + 1024 x + 256 ) d x}{x ^{8} + 16 x ^{7} + 112 x ^{6} + 448 x ^{5} + 1120 x ^{4} + 1792 x ^{3} + 1792 x ^{2} + 1024 x + 256}

\int_{0}^{3} 4 x d x

x \to - 1 lim (\frac{x ^{2} + x}{x + 1})

(2 x + y) d x + (x - 2 y) d y = 0

(ln (e^{x}))^{^{'}}

What is the solution for (dy)/(dx)+(8y)/(x+2)=(x+2)^6 ?
The solution for (dy)/(dx)+(8y)/(x+2)=(x+2)^6 is