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

Lösung

\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}

Schritte zur Lösung

\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 5 sec^{6} (x) d x

\int_{3}^{8} \frac{x}{x ^{2} - 1} d x

\int cos (x - 2 y) d x

\int_{0}^{\infty} x e^{- \frac{x}{3}} d x

y^{^{''}} + 12 y^{^{'}} + 35 y = 70 t^{2} + 48 t + 4 + 48 e^{t}