6y^'=x^2

Lösung

6 y^{^{'}} = x^{2}

y = \frac{x ^{3}}{18} + c_{1}

Schritte zur Lösung

6 y^{'} (x) = x^{2}

Isoliere

y^{'} (x) : y^{'} (x) = \frac{x ^{2}}{6}

Wenn

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

dann

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

y = \int \frac{x ^{2}}{6} d x

\int \frac{x ^{2}}{6} d x = \frac{x ^{3}}{18} + c_{1}

y = \frac{x ^{3}}{18} + c_{1}

\frac{d}{d x} (\frac{1}{3} x^{3} - x^{2} - 8 x + 1)

y^{^{'}} = \frac{2 x ^{4} + y ^{4}}{x y ^{3}}

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

y^{^{'}} = 9 x + y - 9

\int \frac{x}{x - 6} d x