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8 lines
583 B
TeX
8 lines
583 B
TeX
\newsectionNoPB
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\subsection{Linear differential equations of first order}
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\shade{gray}{Finding solution set} \bi{(1)} Find basis $\{ f_1, \ldots, f_k \}$ for $\mathcal{S}_0$ for homogeneous equation (set $b(x) = 0$).
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\bi{(2)} If inhom. find $f_p$ that solves the equation. The set of solutions $\mathcal{S}_b = \{ f_h + f_p \divides f_h \in \mathcal{S_0} \}$.
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\bi{(3)} If initial conditions, find equations $\in \mathcal{S}_b$ which fulfill conditions using SLE (as always)
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\shortproposition Solution of $y' + ay = 0$ is of form $f(x) = z e^{-A(x)}$ with $A$ anti-derivative of $a$
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