(2x+5)y^'+10y=10(2x+5)

Lösung

(2 x + 5) y^{^{'}} + 10 y = 10 (2 x + 5)

y = \frac{10 ( 16 x ^{6} + 240 x ^{5} + 1500 x ^{4} + 5000 x ^{3} + 9375 x ^{2} + 9375 x )}{3 ( 32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125 )} + \frac{c _{1}}{32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125}

Schritte zur Lösung

(2 x + 5) y^{'} (x) + 10 y = 10 (2 x + 5)

Solve linear ODE:

y = \frac{10 ( 16 x ^{6} + 240 x ^{5} + 1500 x ^{4} + 5000 x ^{3} + 9375 x ^{2} + 9375 x )}{3 ( 32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125 )} + \frac{c _{1}}{32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125}

y = \frac{10 ( 16 x ^{6} + 240 x ^{5} + 1500 x ^{4} + 5000 x ^{3} + 9375 x ^{2} + 9375 x )}{3 ( 32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125 )} + \frac{c _{1}}{32 x ^{5} + 400 x ^{4} + 2000 x ^{3} + 5000 x ^{2} + 6250 x + 3125}

n = 0 \sum \infty \frac{3}{5 ^{n}}

\int (x^{2} - 2 x) d x

\int sec^{2} (3 x + 1) d x

\frac{d}{d x} (7 (e^{x} cos (x) - e^{x} sin (x)))

d er i v a t i v e 3 (x^{2} - 1)^{2}