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chp07/subsections/7.11.html

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@@ -523,11 +523,11 @@ <h2>7.11.2 微分方程类型总结表</h2>
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<td><strong>伯努利方程</strong></td>
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<td>$$y' + P(x)y = Q(x)y^n$$</td>
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<td>换元法</td>
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<td>设 $z = y^{1-n}$</td>
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<td>设 $z = y^{1-n}$<br>$\frac{dz}{dx} + (1-n)P(x)z = (1-n)Q(x)$</td>
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<td>$$n \neq 0, 1$$</td>
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</tr>
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<tr>
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<td><strong><a href="7.7.html">常系数线性</a></strong></td>
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<td><strong><a href="7.8.html">常系数线性</a></strong></td>
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<td>$$y'' + py' + qy = f(x)$$</td>
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<td>特征方程法</td>
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<td>$$r^2 + pr + q = 0$$</td>
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<td><strong><a href="7.9.html">欧拉方程</a></strong></td>
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<td>$$x^2y'' + pxy' + qy = 0$$</td>
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<td>换元法</td>
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<td>设 $x = e^t$</td>
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<td>设 $x = e^t$<br>$\frac{d^2y}{dt^2} + (p-1)\frac{dy}{dt} + qy = 0$</td>
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<td>$$x > 0$$</td>
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</tr>
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</tbody>

chp07/subsections/7.9.html

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@@ -928,7 +928,7 @@ <h4>习题3 <span class="difficulty very-hard">很难</span></h4>
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</div>
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<footer>
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<p>&copy; 2024 高等数学复习系统 | 专注于数学可视化教学</p>
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<p>&copy; 2024 高等数学复习系统 - 欧拉方程</p>
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</footer>
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</div>
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