(dy)/(dx)y=(8x^2-16+16)e^x

Lösung

\frac{d y}{d x} y = (8 x^{2} - 16 + 16) e^{x}

y = 16 (x^{2} e^{x} - 2 (x e^{x} - e^{x})) + c_{1}, y = - 16 (x^{2} e^{x} - 2 (x e^{x} - e^{x})) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} y = (8 x^{2} - 16 + 16) e^{x}

Solve separable ODE:

y = 16 (x^{2} e^{x} - 2 (x e^{x} - e^{x})) + c_{1}, y = - 16 (x^{2} e^{x} - 2 (x e^{x} - e^{x})) + c_{1}

y = 16 (x^{2} e^{x} - 2 (x e^{x} - e^{x})) + c_{1}, y = - 16 (x^{2} e^{x} - 2 (x e^{x} - e^{x})) + c_{1}

d er i v a t i v e (1 + 2 x^{2}) (x - x^{2})

d er i v a t i v e (x^{3} + 8 x)^{3}

\int_{0}^{\frac{π}{2}} π sin^{2} (x) d x

\frac{d}{d x} (7 + 7 x)

\frac{\partial}{\partial y} (4 x - 4 y)