⑩天掌 Teaching Plan on Advanced Mathematics o 例2求微分方程(1+x2)y"=2xy满足初始条件 yn=1,y-=3的特解 解设y=n,代入方程并分离变量得 dp 2x d x p 1+x 两端积分,得l川=l+x2)+C 即 P=y=C1(1+x2)(C1=±e) tianjin polytechnic dmivendityTianjin Polytechnic University Teaching Plan on Advanced Mathematics 例2 求微分方程 (1+ x ) y  = 2xy  2 满足初始条件 1, 3 0 0 =  = x= x= y y 的特解. 解 设y  = p,代入方程并分离变量得 dx x x p dp 2 1 2 + = 两端积分，得 ln p = ln(1+ x ) + C 2 即 (1 ) 2 1 p = y  = C + x ( ) 1 c C = e