⑩天掌 Teaching Plan on Advanced Mathematics o tan∠OMN=tan∠NMR, y 由夹 R 角正/an∠ON=y x切公 式得 tn∠NMR=t 得微分方程 yy2+2xy-y=0,即y=-±,()2+1 tianjin polytechnic dmivendity
Tianjin Polytechnic University Teaching Plan on Advanced Mathematics = − − − = y NMR xy y x y y OMN 1 tan 1 1 tan 2 0, 2 yy + xy − y = 得微分方程 ( ) 1. 2 = − + y x y x 即 y tanOMN = tanNMR, 由夹 角正 切公 式得 x y o M T N R L
⑩天掌 Teaching Plan on Advanced Mathematics o 令=,得u+x d-1±√1+u u L 分离变量 (1+u2)±+/ 令1+u2=t2, t(t±1)x 积分得ln±1=n,即√2+1 ±1, tianjin polytechnic dmivendity
Tianjin Polytechnic University Teaching Plan on Advanced Mathematics 令 ， x y u = , 1 1 2 u u dx du u x − + 得 + = 分离变量 , (1 ) 1 2 2 x dx u u udu = − + + 令1+ u 2 = t 2 ， , ( 1) x dx t t tdt = − 积分得 ln 1 ln , x C t = 1 1, 2 + = x C 即 u