erweitern y'(x)(x)^2-(3y^2+cos(x)y'(x)+3y^2cos(x)=0)

Lösung

erweitern

y^{'} (x) (x)^{2} - (3 y^{2} + cos (x) y^{'} (x) + 3 y^{2} cos (x) = 0)

x^{2} y' (x) - 3 y^{2} - cos (x) y' (x) - 3 cos (x) y^{2} = 0

Schritte zur Lösung

y^{'} (x) (x)^{2} - (3 y^{2} + cos (x) y^{'} (x) + 3 y^{2} cos (x) = 0)

= (x)^{2} y^{^{'}} (x) - (3 y^{2} + cos (x) y^{^{'}} (x) + 3 \cdot 0 = cos (x) y^{2})

- (3 y^{2} + cos (x) y^{'} (x) + 3 y^{2} cos (x) = 0) : - 3 y^{2} - cos (x) y^{'} (x) - 3 y^{2} cos (x) = 0

y^{'} (x) (x)^{2} - 3 y^{2} - cos (x) y^{'} (x) - 3 y^{2} cos (x) = 0

Multipliziere aus

y^{'} (x) (x)^{2} - 3 y^{2} - cos (x) y^{'} (x) - 3 y^{2} cos (x) : x^{2} y^{'} (x) - 3 y^{2} - cos (x) y^{'} (x) - 3 cos (x) y^{2}

x^{2} y^{^{'}} (x) - 3 y^{2} - cos (x) y^{^{'}} (x) - 3 cos (x) y^{2} = 0

e x p an d - \frac{( - L + 3 x ) ( - 2 L + 3 x ) ( - L + x )}{2 L ^{3}}

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

e x p an d x + 3 (x - 1 = 6 - 4 (2 x + 3))

e x p an d 28 (e^{- 0.05 t} - e^{- 0.21 t})

e x p an d cos (4 t) h (t - \frac{7 π}{4})