式子转化:y^2+x^2(dy/dx)=xy(dy/dx)y^2+x^2(dy/dx)=xy(dy/dx) 原方程可写成dy/dx=y^2/(xy-x^2) 对怎么分离dy/dx和y^2/(xy-x^2) 能说下吗,
来源：学生作业帮助网 编辑：六六作业网 时间：2024/12/23 15:43:19
式子转化:y^2+x^2(dy/dx)=xy(dy/dx)y^2+x^2(dy/dx)=xy(dy/dx)原方程可写成dy/dx=y^2/(xy-x^2)对怎么分离dy/dx和y^2/(xy-x^2)
式子转化:y^2+x^2(dy/dx)=xy(dy/dx)y^2+x^2(dy/dx)=xy(dy/dx) 原方程可写成dy/dx=y^2/(xy-x^2) 对怎么分离dy/dx和y^2/(xy-x^2) 能说下吗,
式子转化:y^2+x^2(dy/dx)=xy(dy/dx)
y^2+x^2(dy/dx)=xy(dy/dx) 原方程可写成dy/dx=y^2/(xy-x^2) 对怎么分离dy/dx和y^2/(xy-x^2) 能说下吗,
式子转化:y^2+x^2(dy/dx)=xy(dy/dx)y^2+x^2(dy/dx)=xy(dy/dx) 原方程可写成dy/dx=y^2/(xy-x^2) 对怎么分离dy/dx和y^2/(xy-x^2) 能说下吗,
dy/dx=y^2/(xy-x^2),分子分母同时除以x^2
即dy/dx=(y/x)^2 / (y/x -1)
这时令y/x=u,
那么y=ux,所以dy/dx=u+x*du/dx,
代入得到u+x*du/dx= u^2/(u-1),
即x*du/dx=u/(u-1),
所以(1 -1/u)*du=1/x *dx,
两边积分得到u-lnu =lnx+C,(C为常数)
即u=ln(ux),带回y/x=u,
故y/x=lny+C,(C为常数) 隐函数也不必再化简了
对于这种可以转换得到dy/dx=f(y/x)形式的微分方程称为齐次方程,
就是要令u=y/x,这样转换来解
式子转化:y^2+x^2(dy/dx)=xy(dy/dx)y^2+x^2(dy/dx)=xy(dy/dx) 原方程可写成dy/dx=y^2/(xy-x^2) 对怎么分离dy/dx和y^2/(xy-x^2) 能说下吗,
(x^2)dy+（y^2)dx=dx-dy
求下列式子dy/dx (1) x^2y-x+y=0；(2) x√y =y-11
微分方程 dy/dx=(-2x)/y
解方程y^2+x^2*(dy/dx)=x*y*(dy/dx)
dy/dx=x/2y dy/dx=x+y
dy/dx=2y/x+3x/2y
x^y-y^x=2,求dy/dx
求dy/dx=(x-y+5)/(x+y-2)
（-2x-y+9)dy=(-y+x+3)dx
dy/dx,y=(1+x+x^2)e^x
Y=2-sinx.求dy/dx及dy/dx|x=0
d^2y/dx^2=(dy/dx)'×(dy/dx),另外请解释下dx,dy的含义,dx和dy是指x=...和y=...的式子吗（比如参数方程）?还是x的导数和y的导数...我这块很混乱...
y=[sin(x^4)]^2,则dy/dx=?,dy^2/dx^2=?,dy/d(x^2)=?
x^2+y^2=e^y求dy/dx
求dy/dx=x/y+(cosx/y)^2通解
dy/dx=x(1+y^2)/y通解
微分方程dy/dx=y/(x+y^2)的通解?