(2xy^2-7)dx+(2x^2y+6)dy=0

Lösung

(2 x y^{2} - 7) d x + (2 x^{2} y + 6) d y = 0

y = \frac{- 3 + - x ^{2} ( - 7 x - c _{1} ) + 9}{x ^{2}}, y = - \frac{- x ^{2} ( - 7 x - c _{1} ) + 9 + 3}{x ^{2}}

Schritte zur Lösung

(2 x y^{2} - 7) d x + (2 x^{2} y + 6) d y = 0

Solve exact ODE:

y = \frac{- 3 + - x ^{2} ( - 7 x - c _{1} ) + 9}{x ^{2}}, y = - \frac{- x ^{2} ( - 7 x - c _{1} ) + 9 + 3}{x ^{2}}

y = \frac{- 3 + - x ^{2} ( - 7 x - c _{1} ) + 9}{x ^{2}}, y = - \frac{- x ^{2} ( - 7 x - c _{1} ) + 9 + 3}{x ^{2}}

\frac{d}{d x} (ln (\frac{e ^{x}}{e ^{x} - 1}))

t an g e n t f (x) = x - 1, at x = 10

d er i v a t i v e \frac{e ^{x}}{e ^{x} - e ^{- x}}

(\frac{d y}{d x}) + 2 y = e^{- x}

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