1.求下列方程的解:-|||-(1) dfrac (dy)(dx)=2xy ,并求满足初值条件 x=0 ,y=1 的特解;-|||-(2) ^2dx+(x+1)dy=0 ,并求满足初值条件 x=0 ,y=1 的特解;-|||-(3) dfrac (dy)(dx)=dfrac (1+{y)^2}(xy+{x)^3y}-|||-(4) (1+x)ydx+(1-y)xdy=0 ;-|||-(5) (y+x)dy+(x-y)dx=0 ;-|||-(6) dfrac (dy)(dx)-y+sqrt ({x)^2-(y)^2}=0 ;-|||-(7) tan ydx-cot xdy=0 ;1.求下列方程的解:-|||-(1) dfrac (dy)(dx)=2xy ,并求满足初值条件 x=0 ,y=1 的特解;-|||-(2) ^2dx+(x+1)dy=0 ,并求满足初值条件 x=0 ,y=1 的特解;-|||-(3) dfrac (dy)(dx)=dfrac (1+{y)^2}(xy+{x)^3y}-|||-(4) (1+x)ydx+(1-y)xdy=0 ;-|||-(5) (y+x)dy+(x-y)dx=0 ;-|||-(6) dfrac (dy)(dx)-y+sqrt ({x)^2-(y)^2}=0 ;-|||-(7) tan ydx-cot xdy=0 ;

1.求下列方程的解:-|||-(1) dfrac (dy)(dx)=2xy ,并求满足初值条件 x=0 ,y=1 的特解;-|||-(2) ^2dx+(x+1)

1.求下列方程的解:-|||-(1) dfrac (dy)(dx)=2xy ,并求满足初值条件 x=0 ,y=1 的特解;-|||-(2) ^2dx+(x+1)

2.求下列齐次方程满足所给初值条件的特解:-|||-(1) ((y)^2-3(x)^2)dy+2xydx=0 |x=0=1;-|||-(2) =dfrac (x

2.求下列齐次方程满足所给初值条件的特解：(1)(y^2-3x^2)dy+2xydx=0,y|_(x=0)=1；2.求下列齐次方程满足所给初值条件的特解：$(1

三、填空题-|||-1.微分方程 dfrac (dy)(dx)=1-x+(y)^2-x(y)^2 满足初始条件 |x=0 的特解为 __-|||-2.微分方程

1.设 sin y+(e)^x-x(y)^2=0 ,求 dfrac (dy)(dx) .

1.求下列齐次方程的通解:-|||-(1) -y-sqrt ({y)^2-(x)^2}=0;-|||-(2) dfrac (dy)(dx)=ycdot dfra

2.求下列微分方程满足所给初值条件的特解:-|||-(1) =(e)^2x-y, (|)_(x=0)=0;

求方程 dfrac (dy)(dx)=2x-1-3(y)^2 通过点dfrac (dy)(dx)=2x-1-3(y)^2 的第二次近似解.dfrac (dy)(

2.求下列齐次方程满足所给初值条件的特解:-|||-(2) =dfrac (x)(y)+dfrac (y)(x) (|)_(x=1)=2 ;