(dy)/(dx)=(3ex-9e-x)^2

Lösung

\frac{d y}{d x} = (3 e x - 9 e - x)^{2}

y = 3 e^{2} x^{3} - 27 e^{2} x^{2} - 2 e x^{3} + 9 e x^{2} + \frac{x ^{3}}{3} + 81 e^{2} x + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = (3 e x - 9 e - x)^{2}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = (3 e x - 9 e - x)^{2}

Wenn

f^{^{'}} (x) = g (x)

dann

f (x) = \int g (x) d x

y = \int (3 e x - 9 e - x)^{2} d x

\int (3 e x - 9 e - x)^{2} d x = 3 e^{2} x^{3} - 27 e^{2} x^{2} - 2 e x^{3} + 9 e x^{2} + \frac{x ^{3}}{3} + 81 e^{2} x + c_{1}

y = 3 e^{2} x^{3} - 27 e^{2} x^{2} - 2 e x^{3} + 9 e x^{2} + \frac{x ^{3}}{3} + 81 e^{2} x + c_{1}