(5xy^2-3)dx+(5x^2y+4)dy=0

Lösung

(5 x y^{2} - 3) d x + (5 x^{2} y + 4) d y = 0

y = \frac{- 8 + 64 - 20 x ^{2} ( - 6 x - c _{1} )}{10 x ^{2}}, y = \frac{- 8 - 64 - 20 x ^{2} ( - 6 x - c _{1} )}{10 x ^{2}}

Schritte zur Lösung

(5 x y^{2} - 3) d x + (5 x^{2} y + 4) d y = 0

Solve exact ODE:

y = \frac{- 8 + 64 - 20 x ^{2} ( - 6 x - c _{1} )}{10 x ^{2}}, y = \frac{- 8 - 64 - 20 x ^{2} ( - 6 x - c _{1} )}{10 x ^{2}}

y = \frac{- 8 + 64 - 20 x ^{2} ( - 6 x - c _{1} )}{10 x ^{2}}, y = \frac{- 8 - 64 - 20 x ^{2} ( - 6 x - c _{1} )}{10 x ^{2}}

(x, y) \to (0, 0) lim (x^{3} y)

s im pl i f y \frac{3}{12} x^{4} + \frac{2}{6} x^{3} - x^{2} + 1

\frac{d}{d x} (\frac{6 x}{( x ^{2} + 3 ) ^{2}})

t an g e n t - \frac{1}{2} x^{2} - 2 x + 3

\frac{d}{d x} (\frac{1}{x} - \frac{4}{x ^{3}})