(dy)/(dx)+6x^2y-9x^2=0

Lösung

\frac{d y}{d x} + 6 x^{2} y - 9 x^{2} = 0

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

Schritte zur Lösung

\frac{d y}{d x} + 6 x^{2} y - 9 x^{2} = 0

Solve separable ODE:

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

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

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

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

y^{^{'}} = \frac{y}{x ^{2} + 1}

(x^{2} - 9) y^{^{'}} + x y = 0

y^{^{'}} = \frac{2 y ^{2}}{x ^{2}}