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Update higherMathematics.md
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870138612 authored Nov 6, 2024
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Showing 1 changed file with 10 additions and 10 deletions.
20 changes: 10 additions & 10 deletions src/note/higherMathematics.md
Original file line number Diff line number Diff line change
Expand Up @@ -815,11 +815,11 @@ $$
特解要设为y^*=e^{\alpha x}Q_n(x)x^k,\\
其中
\begin{cases}
e^{ax}照抄,\\
Q_n(x)为x的n次多项式,\\
e^{ax}照抄\\
Q_n(x)为x的n次多项式\\
k=\begin{cases}
0,\alpha 不是特征根,\\
1,\alpha是单特征根,\\
0,\alpha 不是特征根\\
1,\alpha是单特征根\\
2,\alpha是二重特征根.
\end{cases}
\end{cases}.
Expand All @@ -830,10 +830,10 @@ $$
特解要设为y^*=e^{\alpha x}[Q_l^{(1)}(x)\cos \beta x+Q_l^{(2)}\sin \beta x]x^k,\\
其中
\begin{cases}
e^{ax}照抄,\\
Q_l(x)为x的l次多项式,l=\max\{m,n\}\\
e^{ax}照抄\\
Q_l(x)为x的l次多项式l=\max\{m,n\}\\
k=\begin{cases}
0,\alpha\pm \beta \text i不是特征根,\\
0,\alpha\pm \beta \text i不是特征根\\
1,\alpha\pm \beta \text i是特征根.
\end{cases}
\end{cases}.
Expand All @@ -851,17 +851,17 @@ $$

$$
若r为单实根,写\\
Ce^{rx};
Ce^{rx}
$$

$$
若r为k重实根,写\\
(C_1+C_2x+C_3x^2+...+C_kx^{k-1})e^{rx};
(C_1+C_2x+C_3x^2+...+C_kx^{k-1})e^{rx}
$$

$$
若r为单复根\alpha\pm\beta \text{i},写\\
e^{ax}(C_1\cos\beta x+ C_2 \sin\beta x);
e^{ax}(C_1\cos\beta x+ C_2 \sin\beta x)
$$

$$
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