微积方程问题```有能耐的人进```
(2x-y)dx+(y-x)dy=0
感激不尽```
我初中没毕业```
这个问题是我帮人问的```
人气:131 ℃ 时间:2020-04-18 06:15:34
解答
【1】最简便的方法,用matlab解.
>> y=dsolve('(2*t-y)+(y-t)*Dy=0')
y =
[ t+(-t^2+exp(C1)^2)^(1/2)]
[ t-(-t^2+exp(C1)^2)^(1/2)]
即:
y=
[ x+(-x^2+exp(C1)^2)^(1/2)]
[ x-(-x^2+exp(C1)^2)^(1/2)]
【2】用scrodinger 的方法
2xdx+ydy-ydx-xdy=0
d(2x^2+y^2-2xy)=0
2x^2+y^2-2xy-c=0
判别式=4x^2-4*(2x^2-c)=-4x^2-4c
y1=[2x+(-4x^2-4c)^(1/2)]/2=x+(-x^2-c)^(1/2)
y2=[2x-(-4x^2-4c)^(1/2)]/2=x-(-x^2-c)^(1/2)
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