å·²ç¥æ¹ç¨F(xï¼y)=0è½ç¡®å®å½æ°y=y(x)ï¼é£ä¹æ¹ç¨ä¸¤è¾¹å¯¹xå导æ°å¾ï¼
∂F/∂x+(∂F/∂y)(dy/dx)=0
æ dy/dx=-(∂F/∂x)/(∂F/∂y);
ä¾å¦ï¼å·²ç¥æ¹ç¨F(xï¼y)= xy³+xe^y+3x+siny=0è½åå¾å½æ°y=y(x);
å¦ä¸è§£æ³ï¼æ¹ç¨ä¸¤è¾¹å¯¹xå导æ°ï¼å¾ï¼
y³+3xy²y'+e^y+x(e^y)y'+3+(cosy)y'=0
(3xy²+xe^y+cosy)y'=-(y³+e^y+3)
â´y'=-(y³+e^y+3)/(3xy²+xe^y+cosy)
ç¨æ¤æ³æ¶ï¼è¦è®°ä½ï¼y³ï¼e^yï¼cosyé½æ¯yçå½æ°ï¼èyåæ¯xçå½æ°ï¼å æ¤å°å®ä»¬å¯¹xæ±å¯¼æ¶ï¼
è¦ç¨å¤åå½æ°çé¾å¼æ±å¯¼è§åï¼å³d(xy³)/dx=∂(xy³)/∂x=[y³+x(∂y³/∂y)(∂y/∂x)]=y³+3xy²y';
å ¶å®ç±»ä¼¼ã