(6xdy)/(dx)=2xe^x-6y+6x^2

Lösung

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

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

\int e^{2 z} d z

\frac{d}{d x} (arctan (x t))

\frac{\partial}{\partial x} (\frac{3 x}{x ^{2} + 2})

\frac{d}{d x} (8 x^{2} sin (x) tan (x))

\frac{d y}{d x} = \frac{y ^{2} - y}{x}