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演習問題

1. 次の微分方程式の$x = 0$のまわりでの整級数解を求めよ．
\begin{displaymath}\begin{array}{ll} (a) y^{\prime} + y = e^{x} & (b) y^{\pr... ...{x} & (d) y^{\prime\prime} + xy^{\prime} - 4y = 0 \end{array}\end{displaymath}
2. 次の微分方程式の付記した点のまわりでの整級数解を求めよ．
\begin{displaymath}\begin{array}{ll} (a) y^{\prime\prime} + (x-2)y = 0, a =... ...\prime\prime} + (x-1)y^{\prime} + 3y = x^2, a = 1 \end{array}\end{displaymath}