《高等数学（专升本）》 - 西交网校 - 西交网校

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《高等数学（专升本）》

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线性齐次方程解的结构
定理!，若函数j(x)y(x)是二阶线性齐次方程
y"+ P(x)v'+Q(x)y=0
的两个解,则y=Cn(x)+C₂yz(x)(C,Cz为任意常数)也是该方程的解。(叠加原理)
证: 将y=Cy(x)+C2)2(x)代入方程左边，得
[Cjy"+C2y2] +P(x)[Cy' +C2y2 ]
+Q(x)[Cy +C2y2]
=C¡[y"+P(x)y' +Q(x)y]
+C₂[y” +P(x)y+Q(x)y2] =0

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122030243810014 · 2022-04-12 · （视频）第79讲 0