The solution of `xdy=(2y+2x^4+x^2)dx`, is (A) `y=x^4+xlogx+C` (B) `y=x^2+xlogx+C` (C) `y=x^4+x^2logx+C` (D) none of these

The solution of the equation xdy-ydx=sqrt(x^2-y^2)dx subject to the condition y(1)=0 is (A) y=xsin(logx) (B) y=x^2 sin(logx) (C) y=x^2(x-1) (D) none of these

The solution of the equation xdy-ydx=sqrt(x^2-y^2)dx subject to the condition y(1)=0 is (A) y=xsin(logx) (B) y=x^2 sin(logx) (C) y=x^2(x-1) (D) none of these

The solution of (x^2+xy)dy=(x^2+y^2)dx is (A) logx=log(x-y)+y/x+C (B) logx=2log(x-y)+y/x+C (C) logx=log(x-y)+x/y+C (D) none of these

int[1/logx-1/(logx)^2]dx= (A) x/logx (B) xlogx (C) logx/x (D) none of these

The solution of y(2xy+e^x)dx-e^xdy=0 is (A) x^2+ye^(-x)=C (B) xy^2+e^(-x)=C (C) x/y+e^(-x)/x^2=C (D) x^2+e^x/y=C

The solution of y(2xy+e^x)dx-e^xdy=0 is (A) x^2+ye^(-x)=C (B) xy^2+e^(-x)=C (C) x/y+e^(-x)/x^2=C (D) x^2+e^x/y=C

The solution of cos(x+y)dy=dx is (A) y=cos^-1(y/x)+C (B) y=xsec(y/x)+C (C) y=tan((x+y)/2)+C (D) none of these

The solution of cos(x+y)dy=dx is (A) y=cos^-1(y/x)+C (B) y=xsec(y/x)+C (C) y=tan((x+y)/2)+C (D) none of these

The solution of the differential equation (dy/dx)^2-(xdy)/dx+y=0 is (A) y=2 (B) y=2x (C) y=2x-4 (D) y=2x^2-4