¶Ôln2yÇ󵼵öàÉÙ

¶Ôln2yÇóµ¼µÃ=2/2y=1/y¡£»ù´¡Çóµ¼¹«Ê½£ºc'=0(cΪ³£Êý£©(x^a)'=ax^(a-1),aΪ³£ÊýÇÒa¡Ù0 (a^x)'=a^xlna (e^x)'=e^x (...


lny ºÍ ln2yµÄµ¼ÊýÒ»Ñùô

´ð£ºÊÇ ln(2y)=ln2+lny ËùÒÔ£ºlnyºÍln(2y)µÄµ¼Êý¶¼ÊÇÒ»ÑùµÄ,Ïàͬ


...A.ln2x+ln2y=0B.ln2x=ln2yC.ln2x+ln2y=1D.ln2x=ln...

½â´ð:½â:ÓÉ΢·Ö·½³Ìylnxdx=xlnydy,µÃlnxxdx=lnyydyÁ½±ß»ý·Ö,µÃ12(lnx)2=12(lny)2+C¶øy|x=1=1¡àC=0¡àÂú×ãy|x=1=1µÄÌØ½âÊÇln2x=ln2y¹ÊÑ¡:B.


¶Ôln2yÇ󵼵öàÉÙ???¶Ô1/2y»ý·ÖµÃ¶àÉÙ

ln2y=ln2+lny ËùÒÔ ln2yµÄµ¼Êý=1/y¡¤y'


lnx=2y ÄÜÍÆ³öx=ln2yô?ʲôʱºòÄÜÁ½±ßÈ¡¶ÔÊý?

lnx=2y ÄÜÍÆ³öx=ln2yô£¿²»ÄÜ¡£¡£ lnx=2y ÄÜÍÆ³öx=e^2y ___ʲôʱºòÄÜÁ½±ßÈ¡¶ÔÊý£¿µ±µÈʽÁ½±ßµÄÊý¶¼ÊÇÕýÊýµÄʱºò ¾Í¿ÉÒÔÁ½±ßͬʱȡÒÔÒ»¸ö´óÓÚ0ÇÒ²»µÈÓÚ1µÄÊý...


΢·Ö·½³Ìy'=3x^2yµÄͨ½âÔõôÇó

y' = dy/dx = 3x²y=> (1/y)dy = 3x²dx {Á½±ß»ý·Ö}=> ln|y| = x³ - ln|C| {Õâ¸öÈÎÒâ³£ÊýµÄÐÎʽÊÇÒª¿´¾ßÌåÐÎʽ´ÕµÄ}=> ln|Cy| ...


ln2yÊÇÄĸöº¯ÊýµÄµ¼Êý

ÄãÒªÏÈ˵yÊÇË­µÄº¯Êý£¬ ²»È»Ôõô֪µÀÊǶÔxÇóµ¼µÃln2y»¹ÊǶÔyÇóµ¼µÃln2y£¬Èç¹ûÊǶÔyÇóµ¼µÃln2y ÔòÔ­º¯ÊýÊÇ yln2y - y + c


¡¾¼±¡¿ÇóÓɲÎÊý·½³Ì×é{x=ln¸ùºÅ(1+t^2),y=arctantËù...

ÊÓÆµ½â´ðÌâÄ¿¾Ù±¨¡¾¼±¡¿ÇóÓɲÎÊý·½³Ì×é{x=ln¸ùºÅ(1+t^2),y=arctantËùÈ·¶¨º¯ÊýµÄÒ»½×µ¼Êýdy/dxºÍ¶þ½×µ¼Êýd^2y/dx^2 ɨÂëÏÂÔØ×÷Òµ°ï ËÑË÷´ðÒÉÒ»ËѼ´µÃ´ð°¸½âÎö ²é¿´¸ü¶àÓÅÖʽâÎö½â´ðÒ»¾Ù±¨´ð:x=ln¡Ì(1+t^2),dx/dt=[1/¡Ì(1+t^2)]*(1/2)*2t/¡Ì(1+t^2)=t/(1+t^2)y=arctant,dy/dt=1/(1+t^2)ËùÒÔ:dy/dx=1/...


ln(2y)=lnx+C,yµÈÓÚ¶àÉÙ?

½â£º·½³ÌΪln(2y)=lnx+C£¬»¯Îªln(2y/x)=C£¬2y/x=eᶜy=0.5xeᶜ


Ïà¹ØËÑË÷

ÈÈÃÅËÑË÷