麻烦帮我看下这道高数题解法错哪了微分方程1/(x^2)y''=lnx的通解:参考答案是y=(x^4/12)lnx-(7/144)x^4+C1x+C2y''=(x^2)ln2u=x^2 du=2xdxv=lnx dv=1/xdxy'=x^2lnx-2∫lnx.xdx+C1y=x^2lnx-lnx-2(lnx.(x^2/2)-∫x^2(1/xdx)+C1x+C2=x^2/4
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![麻烦帮我看下这道高数题解法错哪了微分方程1/(x^2)y''=lnx的通解:参考答案是y=(x^4/12)lnx-(7/144)x^4+C1x+C2y''=(x^2)ln2u=x^2 du=2xdxv=lnx dv=1/xdxy'=x^2lnx-2∫lnx.xdx+C1y=x^2lnx-lnx-2(lnx.(x^2/2)-∫x^2(1/xdx)+C1x+C2=x^2/4](/uploads/image/z/15001259-59-9.jpg?t=%E9%BA%BB%E7%83%A6%E5%B8%AE%E6%88%91%E7%9C%8B%E4%B8%8B%E8%BF%99%E9%81%93%E9%AB%98%E6%95%B0%E9%A2%98%E8%A7%A3%E6%B3%95%E9%94%99%E5%93%AA%E4%BA%86%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B1%2F%28x%5E2%29y%27%27%3Dlnx%E7%9A%84%E9%80%9A%E8%A7%A3%EF%BC%9A%E5%8F%82%E8%80%83%E7%AD%94%E6%A1%88%E6%98%AFy%3D%EF%BC%88x%5E4%2F12%29lnx-%287%2F144%29x%5E4%2BC1x%2BC2y%27%27%3D%28x%5E2%29ln2u%3Dx%5E2+du%3D2xdxv%3Dlnx+dv%3D1%2Fxdxy%27%3Dx%5E2lnx-2%E2%88%ABlnx.xdx%2BC1y%3Dx%5E2lnx-lnx-2%28lnx.%28x%5E2%2F2%29-%E2%88%ABx%5E2%281%2Fxdx%29%2BC1x%2BC2%3Dx%5E2%2F4)
麻烦帮我看下这道高数题解法错哪了微分方程1/(x^2)y''=lnx的通解:参考答案是y=(x^4/12)lnx-(7/144)x^4+C1x+C2y''=(x^2)ln2u=x^2 du=2xdxv=lnx dv=1/xdxy'=x^2lnx-2∫lnx.xdx+C1y=x^2lnx-lnx-2(lnx.(x^2/2)-∫x^2(1/xdx)+C1x+C2=x^2/4
麻烦帮我看下这道高数题解法错哪了
微分方程1/(x^2)y''=lnx的通解:参考答案是y=(x^4/12)lnx-(7/144)x^4+C1x+C2
y''=(x^2)ln2
u=x^2 du=2xdx
v=lnx dv=1/xdx
y'=x^2lnx-2∫lnx.xdx+C1
y=x^2lnx-lnx-2(lnx.(x^2/2)-∫x^2(1/xdx)+C1x+C2
=x^2/4-lnx+C1x+C2
麻烦帮我看下这道高数题解法错哪了微分方程1/(x^2)y''=lnx的通解:参考答案是y=(x^4/12)lnx-(7/144)x^4+C1x+C2y''=(x^2)ln2u=x^2 du=2xdxv=lnx dv=1/xdxy'=x^2lnx-2∫lnx.xdx+C1y=x^2lnx-lnx-2(lnx.(x^2/2)-∫x^2(1/xdx)+C1x+C2=x^2/4
原题是 1/(x^2)y''=lnx,不是y''=(x^2)ln2
y''=(x^2)lnx
积分:y'=(x^3 /3)lnx - x^3 /9 +C1 (分部积分)
再积分一次,得:y =(x^4 /12)lnx - x^4 /48 - x^4 /36 +C1x+C2 (分部积分)
即:y=(x^4/12)lnx-(7/144)x^4+C1x+C2