(xdy)/(x^(2)+y^(2))=((y)/(x^(2)+y^(2))-1)dx

Match the following {:(,"List-I",,"List-II",),((1),"The equation of family of curves for which",(a),y+e^(-x) = " c, y " - e^(x) = c,),(,"length of the normal = The radius vector.",,,),((2),"Solution of the differential equation " ((dy)/(dx))^(2) - (dy)/(dx)(e^(x)+e^(-x))+1=0 " is",(b),y = x cot (x+c),),((3),"The solution of " (xdy)/((x^(2)+y^(2))) = ((y)/(x^(2)+y^(2))-1)dx " is",(c),y^(2)+- x^(2) = k^(2),),(,,(d),e^(y)=e^(x)-1,):}

The solution of the differential equation (1+x^(2)y^(2))ydx+(x^(2)y^(2)-1)xdy=0 is

If y=cos(mcos^(-1)x) , then prove that : (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx+m^(2)y=0 .

If y=e^(m"sin"^(-1)x) , prove that (1-x^(2))(d^(2)y)/(dx^(2))-xdy/(dx)=m^(2)y

The solution of e^(x((y^(2)-1))/(y)){xy^(2)dy+y^(3)dx}+{ydx-xdy}=0 , is

The solution of e^(x((y^(2)-1))/(y)){xy^(2)dy+y^(3)dx}+{ydx-xdy}=0 , is

The solution of e^(x((y^(2)-1))/(y)){xy^(2)dy+y^(3)dx}+{ydx-xdy}=0 , is

The solution of e^(x((y^(2)-1))/(y)){xy^(2)dy+y^(3)dx}+{ydx-xdy}=0 , is

The solution of e^(x((y^(2)-1))/(y)){xy^(2)dy+y^(3)dx}+{ydx-xdy}=0 , is

If y=e^(a cos^(-1)x),-2lexle1 , show that (1-x^(2))(d^(2)y)/(dx^(2))-xdy/dx-a^(2)y=0