y^'=2x-3xy

Lösung

y^{^{'}} = 2 x - 3 x y

y = \frac{e ^{\frac{- 3 x ^{2} + c _{1}}{2}}}{3} + \frac{2}{3}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{e ^{\frac{- 3 x ^{2} + c _{1}}{2}}}{3} + \frac{2}{3}

y = \frac{e ^{\frac{- 3 x ^{2} + c _{1}}{2}}}{3} + \frac{2}{3}

ln (y^{^{'}}) = y

y y^{^{'}} - x y^{2} + x = 0

(1 + x^{2}) \frac{d y}{d x} = x tan (y)

e^{- y} sin (x) - \frac{d y}{d x} cos^{2} (x) = 0

\frac{d y}{d x} = \frac{17 x y}{( ln ( y ) ) ^{6}}