(x-7)^4y^'+5(x-7)^3y=x+7

Lösung

(x - 7)^{4} y^{^{'}} + 5 (x - 7)^{3} y = x + 7

y = \frac{x ^{3}}{3 ( x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807 )} - \frac{49 x}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807} + \frac{c _{1}}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807}

Schritte zur Lösung

(x - 7)^{4} y^{'} (x) + 5 (x - 7)^{3} y = x + 7

Solve linear ODE:

y = \frac{x ^{3}}{3 ( x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807 )} - \frac{49 x}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807} + \frac{c _{1}}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807}

y = \frac{x ^{3}}{3 ( x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807 )} - \frac{49 x}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807} + \frac{c _{1}}{x ^{5} - 35 x ^{4} + 490 x ^{3} - 3430 x ^{2} + 12005 x - 16807}

\int \frac{1}{tan ( y )} d y

y^{^{''}} - 8 y^{^{'}} + 16 y = t^{- 7} e^{4 t}

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

x \to 5 lim (\frac{x}{x - 5})

\int \frac{1}{y ^{\frac{1}{3}}} d y