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

解

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

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

解答ステップ

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

代用

\frac{d y}{d x}

と

y^{'} (x)

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

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

であれば

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}