(dy)/(dx)=-x^4-4x^3+5x^2

Lösung

\frac{d y}{d x} = - x^{4} - 4 x^{3} + 5 x^{2}

y = - \frac{x ^{5}}{5} - x^{4} + \frac{5 x ^{3}}{3} + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = - x^{4} - 4 x^{3} + 5 x^{2}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = - x^{4} - 4 x^{3} + 5 x^{2}

Wenn

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

dann

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

y = \int - x^{4} - 4 x^{3} + 5 x^{2} d x

\int - x^{4} - 4 x^{3} + 5 x^{2} d x = - \frac{x ^{5}}{5} - x^{4} + \frac{5 x ^{3}}{3} + c_{1}

y = - \frac{x ^{5}}{5} - x^{4} + \frac{5 x ^{3}}{3} + c_{1}