Çó½â΢·Ö·½³ÌÒªÏêϸ²½Öèy'=3xy2

dy/y2=3x dx -1/y=3/2 x^2 +C 3x^2+2/y=c (cΪ³£Êý)


(x^3+y^3)dx - 3xy^2dy=0ÇóÆë´Î·½³ÌµÄͨ½â

µÈʽ(x^3+y^3)dx=3xy^2dyÁ½±ßͬʱ³ýÒÔx^3Ôò¿ÉÒԵõ½[(y/x)^3+1]dx=3(y/x)^2dy ÔÙÁîy=uxÔòdy=udx+xdu´øÈëÇóµÄ(1-2u^3)^(1/2)=(x+c)^2 ...


΢·Ö·ûºÅ,dx,dyµ½µ×ÊÇʲôº¬Òå?

Àý3£¬z=x^2-3xy^2\begin{split} dz &=\{(x+dx)^2-3(x+dx)(y+dy)^2\}-\{x^2-3xy^2\}\\ &=\{[x^2+2xdx+dx^2]-...


Çó΢·Ö·½³Ìͨ½âÇó΢·Ö·½³Ì(3x^2+2xy - y^2)dx+(x^2 - xy...

½â:¡ß(3x²+2xy-y²)dx+(x²-xy)dy=90ͬ³ýÒÔx^2(3+2y/x-(y/x)^2)dx+(1-y/x)dy=0y/x=uy=ux y'=u'x+u(3+2u-u^2)+(1-u)(...


´úÊýʽ3xyµÄ´ÎÊýÊÇ( )A.1B.2C.3D. - 1

½â´ð:½â:¸ù¾Ýµ¥Ïîʽ¶¨ÒåµÃ:´úÊýʽ3xyµÄ´ÎÊýÊÇ2.¹ÊÑ¡B.


(x+y)dx - 3xydy=0µÄͨ½â?

½â´ð x3dx=3xy2dy-y3dx x3dx=xdy3-y3dx xdx=dy3/x+y3d(1/x)ͨ½âx2/2=y3/x+C


...ÓÉ·½³Ìxy^3=y - 1ËùÈ·¶¨,Çódy/dx;2¡¢ÒÑÖªy=arc tan(e^x...

1¡¢Á½±ßͬʱ΢·Ö,y^3dx+3xy^2dy=dy,so dy/dx=(y^3)/(1-3xy^2)2¡¢dy=(e^x)/(1+e^(2x))dx


΢·Ö·ûºÅ dx¡¢dy ±íʾʲôº¬Òå?

±ÈÈç´ó¼ÒϲÎÅÀÖ¼ûµÄf(x,y)=\frac{xy}{x^2+y^2}£ºÓÉÓÚf(x,kx)=\frac{k}{1+k^2}ÓëkÓйأ¬Òò´Ë\lim_{(x,y) \rightarrow (...\, \Delta x \rightarrow 0,µÄ¼«ÏÞÇéÐÎÈËΪ¼Ç×÷dy = f'(x_0) \Delta x = f'(x_0)dx,ÕâÀïµÄº¬ÒåÊDZȽϺ¬»ì²»ÇåµÄ. ´ÓÊýѧµÄ½Ç¶È...


Çó¶þÖØ»ý·ÖDmax(xy,1)dxdy,ÆäÖÐD={(x,y)|0¡Üx¡Ü2...

1 x0dy+ ¡Ò 1 20dx ¡Ò 20dy =( 15 4ln2)+2ln2+1 = 19 4+ln2.ÒòΪµ±xy¡Ü1ʱ,max(xy,1)=1,¶øµ±xy>1ʱ,max(xy,1)=2,¹Ê¸ù¾ÝxyµÄȡֵ·¶Î§ÒÔ¼°¼ÆËãµÄ¼ò±ã...


(3xy+x^2)dy+(y^2+xy)dx=0 Çóͨ½â

==>2y(3xy+x^2)dy+2y(y^2+xy)dx=0 (µÈʽÁ½¶Ëͬ³Ë2y)==>2(3xy^2dy+y^3dx)+2(x^2ydy+xy^2dx)=0 ==>2d(xy^3)+d(x^2y^2)=0 ==>2¡Òd(xy...


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