y(dy)/(dx)+3y=x^2y

Lösung

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

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

Schritte zur Lösung

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

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

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

Isoliere

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

Wenn

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

dann

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

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

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

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

d er i v a t i v e x^{7 x}

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n = 0 \sum \infty \frac{1}{n ^{2} + n + 1}

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

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