求微积方程1.(1+y)dx-(1-x)dy=02.xy'-ylny=03.y'=e^(x+y)4.y-xy‘=a(y^2+y')5.(xy^2+x)dx+(y-x^2y)dx=0参考答案是1.(1-x)(1+y)=c2.y=e^(cx)3.e^x+e^(-y)+c=04.y/(1-ay)=c(a+x)5.(1+y^2)/(1-x^2)=c我算出来的答案与参考答案都不同把过程
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![求微积方程1.(1+y)dx-(1-x)dy=02.xy'-ylny=03.y'=e^(x+y)4.y-xy‘=a(y^2+y')5.(xy^2+x)dx+(y-x^2y)dx=0参考答案是1.(1-x)(1+y)=c2.y=e^(cx)3.e^x+e^(-y)+c=04.y/(1-ay)=c(a+x)5.(1+y^2)/(1-x^2)=c我算出来的答案与参考答案都不同把过程](/uploads/image/z/7647927-15-7.jpg?t=%E6%B1%82%E5%BE%AE%E7%A7%AF%E6%96%B9%E7%A8%8B1.%281%2By%29dx-%281-x%29dy%3D02.xy%27-ylny%3D03.y%27%3De%5E%28x%2By%294.y-xy%E2%80%98%3Da%28y%5E2%2By%27%295.%28xy%5E2%2Bx%29dx%2B%28y-x%5E2y%29dx%3D0%E5%8F%82%E8%80%83%E7%AD%94%E6%A1%88%E6%98%AF1.%EF%BC%881-x%29%281%2By%29%3Dc2.y%3De%5E%28cx%293.e%5Ex%2Be%5E%28-y%29%2Bc%3D04.y%2F%281-ay%29%3Dc%28a%2Bx%295.%281%2By%5E2%29%2F%281-x%5E2%29%3Dc%E6%88%91%E7%AE%97%E5%87%BA%E6%9D%A5%E7%9A%84%E7%AD%94%E6%A1%88%E4%B8%8E%E5%8F%82%E8%80%83%E7%AD%94%E6%A1%88%E9%83%BD%E4%B8%8D%E5%90%8C%E6%8A%8A%E8%BF%87%E7%A8%8B)
求微积方程1.(1+y)dx-(1-x)dy=02.xy'-ylny=03.y'=e^(x+y)4.y-xy‘=a(y^2+y')5.(xy^2+x)dx+(y-x^2y)dx=0参考答案是1.(1-x)(1+y)=c2.y=e^(cx)3.e^x+e^(-y)+c=04.y/(1-ay)=c(a+x)5.(1+y^2)/(1-x^2)=c我算出来的答案与参考答案都不同把过程
求微积方程
1.(1+y)dx-(1-x)dy=0
2.xy'-ylny=0
3.y'=e^(x+y)
4.y-xy‘=a(y^2+y')
5.(xy^2+x)dx+(y-x^2y)dx=0
参考答案是1.(1-x)(1+y)=c
2.y=e^(cx)
3.e^x+e^(-y)+c=0
4.y/(1-ay)=c(a+x)
5.(1+y^2)/(1-x^2)=c
我算出来的答案与参考答案都不同
把过程写得详细点,随便答几题也行啊
求微积方程1.(1+y)dx-(1-x)dy=02.xy'-ylny=03.y'=e^(x+y)4.y-xy‘=a(y^2+y')5.(xy^2+x)dx+(y-x^2y)dx=0参考答案是1.(1-x)(1+y)=c2.y=e^(cx)3.e^x+e^(-y)+c=04.y/(1-ay)=c(a+x)5.(1+y^2)/(1-x^2)=c我算出来的答案与参考答案都不同把过程
(1) (1/1-x)dx=(1/1+y)dy ,-(1/1-x)d1-x=(1/1+y)d1+y ,两面同时积分-ln(1-x)+c1=ln(1+y)+c2,移项
ln(1+y)+ln(1-x)=c3 ,ln(1-x)(1+y)=c3 ,(1-x)(1+y)=e^c3 ,(1-x)(1+y)=c
(2)(I/ylny)dy=1/xdx ,dlnlny=lnx+c2 ,lnlny+c1=lnx+c2 ,lnlny-lnx=c ,lny=cx ,y=e^(cx)
(3)y'=e^x*e^y dy/dx=e^x*e^y e^(-y)dy=e^xdx 两面同时积分 -e^(-y)+c1=e^x+c2 ,e^x+e(-y)+c=0
(4)(a+x)dy/dx=y-ay^2 ,(1/y-ay^2)dy=1/a+xdx ,[1/y+a/(1-ay)]dy=1/(a+x)dx ,lny-ln(1-ay)+c1=ln(a+x)+c2 ,ln(a+x)(1-ay)-lny=c ,(a+x)(1-ay)/y=c(答案和你的一样,只不过是表达形式不一样)
(5)题不对,我也不给你改了,应该能作出来!