(x^2sin(x)+4y)dx+(x)dy=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}}

\int ln (x + (x^{2} - 1)) d x

p a r i t y ln (sec (x) + tan (x))

\int 1 + 9 sin^{2} (3 x) d x

x \to 0 lim (\frac{( x ^{2} - 4 x )}{x})

\int - e^{x} (x + 1) d x