1、 exsin y-2x+(excos y+1)y'=0
2、[x+y2 (y2 - x2)^(1/2)] (dy/dx)=y - xy( y2 - x2)^(1/2)
3、(dy/dx)=x3(y-x)^2 + y•x^(-1)
想了老半天了
拜託教一下吧
Anonymous 寫到:1、 exsin y-2x+(excos y+1)y'=0
2、[x+y2 (y2 - x2)^(1/2)] (dy/dx)=y - xy( y2 - x2)^(1/2)
3、(dy/dx)=x3(y-x)^2 + y•x^(-1)
想了老半天了
拜託教一下吧
lskuo 寫到:Anonymous 寫到:1、 exsin y-2x+(excos y+1)y'=0
2、[x+y2 (y2 - x2)^(1/2)] (dy/dx)=y - xy( y2 - x2)^(1/2)
3、(dy/dx)=x3(y-x)^2 + y•x^(-1)
想了老半天了
拜託教一下吧
Hint:
1. By noticing that [ex sin(y)]' = ex [ sin(y) + y' cos(y) ], one can re-write the equation as the following
[ex sin(y)]' + y' = 2x
Next integrate the both sides.
3. Let z = y/x and solve z.
y' = z +xz' = x5(z-1)2 + z
Now the equation becomes separable.