(dy)/(dx)=7^xln(7)+2/(x^2+1)

Lösung

\frac{d y}{d x} = 7^{x} ln (7) + \frac{2}{x ^{2} + 1}

y = 7^{x} + 2 arctan (x) + c_{1}

Schritte zur Lösung

\frac{d y}{d x} = 7^{x} ln (7) + \frac{2}{x ^{2} + 1}

Ersetze

\frac{d y}{d x}

mit

y^{'} (x)

y^{^{'}} (x) = 7^{x} ln (7) + \frac{2}{x ^{2} + 1}

Wenn

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

dann

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

y = \int 7^{x} ln (7) + \frac{2}{x ^{2} + 1} d x

\int 7^{x} ln (7) + \frac{2}{x ^{2} + 1} d x = 7^{x} + 2 arctan (x) + c_{1}

y = 7^{x} + 2 arctan (x) + c_{1}

\frac{d ^{3}}{d x ^{3}} (\frac{10}{x ^{2}})

\int (- e^{- x}) d x

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} - 3})

i = 0 \sum \infty (\frac{1}{3})^{i}

\frac{\partial}{\partial x} (\frac{1}{1 + x ^{2} + y ^{2}})