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人気のある微分積分 >

(1-t^2)y^{''}-2ty^'+2y=0

解

(1 - t^{2}) y^{^{''}} - 2 t y^{^{'}} + 2 y = 0

解

y = c_{1} - \frac{1}{2} c_{1} t ln (t + 1) + \frac{1}{2} c_{1} t ln (t - 1) + c_{2} t

解答ステップ

(1 - t^{2}) y^{''} (t) - 2 t y^{'} (t) + 2 y = 0

置換を使用して解く:

y = c_{1} - \frac{1}{2} c_{1} t ln (t + 1) + \frac{1}{2} c_{1} t ln (t - 1) + c_{2} t

y = c_{1} - \frac{1}{2} c_{1} t ln (t + 1) + \frac{1}{2} c_{1} t ln (t - 1) + c_{2} t

グラフ

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