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人気のある微分積分 >

(dy)/(dx)+y/(x(x+1))=x+1

解

\frac{d y}{d x} + \frac{y}{x ( x + 1 )} = x + 1

解

y = \frac{c _{1} ( x + 1 )}{x} - \frac{x + 1}{2 x} + \frac{x ( x + 1 )}{2}

解答ステップ

\frac{d y}{d x} + \frac{y}{x ( x + 1 )} = x + 1

線形 ODE を解く:

y = \frac{c _{1} ( x + 1 )}{x} - \frac{x + 1}{2 x} + \frac{x ( x + 1 )}{2}

y = \frac{c _{1} ( x + 1 )}{x} - \frac{x + 1}{2 x} + \frac{x ( x + 1 )}{2}

グラフ

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