实在做不出~求微分方程的通解,就算做两道也帮下我,万分感激.急等(1)xy'-y㏑y=0(2)y'=3(x+y) 此处(x+y)为3的次方(3)xy'=y(㏑y+㏑x)(4)y'+y=e(-x) 此处(-x)为e的次方
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![实在做不出~求微分方程的通解,就算做两道也帮下我,万分感激.急等(1)xy'-y㏑y=0(2)y'=3(x+y) 此处(x+y)为3的次方(3)xy'=y(㏑y+㏑x)(4)y'+y=e(-x) 此处(-x)为e的次方](/uploads/image/z/12673993-49-3.jpg?t=%E5%AE%9E%E5%9C%A8%E5%81%9A%E4%B8%8D%E5%87%BA%7E%E6%B1%82%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B%E7%9A%84%E9%80%9A%E8%A7%A3%2C%E5%B0%B1%E7%AE%97%E5%81%9A%E4%B8%A4%E9%81%93%E4%B9%9F%E5%B8%AE%E4%B8%8B%E6%88%91%2C%E4%B8%87%E5%88%86%E6%84%9F%E6%BF%80.%E6%80%A5%E7%AD%89%EF%BC%881%EF%BC%89xy%27-y%E3%8F%91y%3D0%282%29y%27%3D3%28x%2By%29+%E6%AD%A4%E5%A4%84%EF%BC%88x%2By%EF%BC%89%E4%B8%BA3%E7%9A%84%E6%AC%A1%E6%96%B9%EF%BC%883%EF%BC%89xy%27%3Dy%28%E3%8F%91y%2B%E3%8F%91x%29%284%29y%27%2By%3De%EF%BC%88-x%EF%BC%89+%E6%AD%A4%E5%A4%84%28-x%29%E4%B8%BAe%E7%9A%84%E6%AC%A1%E6%96%B9)
实在做不出~求微分方程的通解,就算做两道也帮下我,万分感激.急等(1)xy'-y㏑y=0(2)y'=3(x+y) 此处(x+y)为3的次方(3)xy'=y(㏑y+㏑x)(4)y'+y=e(-x) 此处(-x)为e的次方
实在做不出~
求微分方程的通解,就算做两道也帮下我,万分感激.急等
(1)xy'-y㏑y=0
(2)y'=3(x+y) 此处(x+y)为3的次方
(3)xy'=y(㏑y+㏑x)
(4)y'+y=e(-x) 此处(-x)为e的次方
实在做不出~求微分方程的通解,就算做两道也帮下我,万分感激.急等(1)xy'-y㏑y=0(2)y'=3(x+y) 此处(x+y)为3的次方(3)xy'=y(㏑y+㏑x)(4)y'+y=e(-x) 此处(-x)为e的次方
(1) xy '=ylny
dy/(ylny)=dx/x
d(lny)/lny=dx/x
ln|lny|=lnx+C
lny=Cx
y=e^(Cx)=Ce^x,C是大于0的任何实数
(2) y '=3^(x+y)
y ' * 3^(-y)=3^x
ln3 * 3^(-y) * dy = ln3 * 3^x * dx
-3^(-y)=3^x+C
(3) xy '=y(lny+lnx)
dy/y=(lny+lnx)dx/x
d(lny)=(lny+lnx)d(lnx)
令u=lny,v=lnx
du=(u+v)dv
u '-u=v
e^(-v)u '-e^(-v)u=e^(-v)v
积分,得
e^(-v)u= -ve^(-v)-e^(-v)+C
u= -v-1+Ce^v
lny= -lnx-1+Cx
(4) y '+y=e^(-x)
e^x * y' + e^x * y=1
积分,得
e^x * y=x+C
y=xe^(-x)+Ce^(-x)