求下列可分离变量型方程的通解或特解：（1)2xy²dx-dy=0;（2)y'=e^x√（1-y²);

(1)2xy'y"=y'²+1;

(2)2xy"=y'²-1;

(3)yy"=2y'²;

(4)y"+y'³=0;

(5)y"e^y'=1;

(6)yy"+y'²=1。

(1)y"+2y'+y=xe^-x;

(2)y"-4y'+3y=1-e^3x;

(3)y"-2y'-3y=6+e^-x，y(0)=0，y'(0)=0;

(4)y"-4y=xe^x，y(0)=1，y'(0)=2;

(5)y"+y'-2y=7cosx-sinx，y(0)=0，y'(0)=1。

(1)(1-4xy)dy=(2y²-3x²)dx;

(2)(3x²y²-4xy)dy+(2xy³-2y²)dx=0;

(3)(x+y²)y'=2x²-y;

(4)xy²dx=(y³-x²y)dy。

(1)y_n+2+3y_n+1=0;

(2)y_n+1-2y_n=2n²-1;

(3)y_n+1-y_n=n+3;

(4)y_n+1-3y_n=3ⁿ;

(5)y_n+1-2y_n=-cos2n;

(6)y_n+1+2y_n=2n-1+eⁿ;

(7)y_n+1+2y_n=3·2ⁿ，y₀=0。

(1)(3x²+6xy²)dx+(6x²y+4y²)dy=0

(2)(a²-2xy-y²)dx-(x+y)²dy=0(a为常数)

(3)e^ydx+(xe^y-2y)dy=0

(4)(xcosy+cosx)y'-ysinx+siny=0

(5)(x²-y)dx-xdy=0

(6)y(x-2y)dx-x²dy=0

(7)(1+e^2θ)dp+2pe^2θdθ=0

(8)(x²+y²)dx+xydy=0