微分方程dy/dx=xy/y^2-x^2 ,当x=0,y=1的特解
微分方程dy/dx=xy/y^2-x^2 ,当x=0,y=1的特解
数学人气：403 ℃时间：2019-12-19 12:54:09
优质解答
dy/dx=xy/(y^2-x^2)y^2dy-x^2dy=xydx(y^2-x^2)dy=xydxx=yu dx=ydu+udy(y^2-y^2u^2)dy=y^2u*(ydu+udy)(1-u^2)dy=uydu+u^2dy(1-2u^2)dy=uydudy/y=udu/(1-2u^2)lny=(-1/4)ln|1-2u^2|+lnCy=C/(1-2u^2)^(1/4)y=C/[1-2(x/y...谢谢 不过答案是y^4-2y^2x^2=1 我也不知道是那里不对……
我来回答
类似推荐
猜你喜欢
- 1I had to call a taxi because the box was
- 2_________ that you lose your job; what would you do then?
- 30.25*1.25*320简便方法计算
- 4已知函数f(x)=lg(1+2^x+4^x*a)/(a^2-a+1),其中a为常数,若当x∈（-∞,1]时,f(x)有意义,求a的取值范围
- 5两个表面积都是24平方厘米的正方体，拼成一个长方体.这个长方体的表面积是（ ）平方厘米. A.48 B.44 C.40 D.16
- 6有一太阳能热水器,水箱的容积为160L,装满水后,若水温由20度升高到70度,水箱里的水的热量是多少、
- 7已知双曲线x²/a²＋y²/b²=1（a>0,b>0）的右焦点为F,
- 8单句改错 now the young man regretted waste so much time when he was at school,
- 9绝对值化简 a+|a+b|-|b-c|-|b+c-a| b＜0,c＜0,a＞0
- 10《数学建模》问题：雪车铲雪问题