xy^3dx+(y+1)e^{-x}dy=0

Lösung

x y^{3} d x + (y + 1) e^{- x} d y = 0

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

Schritte zur Lösung

x y^{3} d x + (y + 1) e^{- x} d y = 0

Solve separable ODE:

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

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

t an g e n t f (x) = x^{2} + 2, at x = 2

d er i v a t i v e - 5 x^{2}

d er i v a t i v e 4 (x^{3} - x)^{4}

\frac{d P}{d t} = 4 Pt, P (1) = 7

\int cos^{3} (6 x s i) n^{- 2} 6 x