(x^2sin(x)+4y)dx+xdy=0

Lösung

(x^{2} sin (x) + 4 y) d x + x d y = 0

y = x cos (x) - 5 sin (x) - \frac{20 cos ( x )}{x} + \frac{60 sin ( x )}{x ^{2}} + \frac{120 cos ( x )}{x ^{3}} - \frac{120 sin ( x )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

Schritte zur Lösung

(x^{2} sin (x) + 4 y) d x + x d y = 0

Solve linear ODE:

y = x cos (x) - 5 sin (x) - \frac{20 cos ( x )}{x} + \frac{60 sin ( x )}{x ^{2}} + \frac{120 cos ( x )}{x ^{3}} - \frac{120 sin ( x )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

y = x cos (x) - 5 sin (x) - \frac{20 cos ( x )}{x} + \frac{60 sin ( x )}{x ^{2}} + \frac{120 cos ( x )}{x ^{3}} - \frac{120 sin ( x )}{x ^{4}} + \frac{c _{1}}{x ^{4}}

\frac{d}{d x} (3^{x^{2} - 1})

\frac{d}{d x} (a t^{5} - 5 b t^{3})

x \to - 2 - lim (2 x + 4 - 2)

\int cos (2 x) tan (2 x) d x

z \to 1 lim (\frac{z + 2}{z ^{4} - 1})