Verify that the given function is a solution of the corresponding differential equation: `y=Ax: xy\'=y (x!=0)`

Verify that the given functions (explicit or implicit is a solution of the corresponding differential equation: y=e^(x)+1:y''-y'=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation : y=Ax : xy'=y(x ne 0)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: 'y =sqrt(1+x^(^^)2):y'=xy/1+x^(^^)2'yquad =quad Ax:xy'=y(x!=0)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: xy=log y+Cvdotsy'=(y^(2))/(1-xy)(xy!=1)

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=sqrt(1+x^(2))y'=(xy)/(1+x^(2))

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=cos x+Cvdotsy'+sin x=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: x+y=tan^(-1)yvdotsy^(2)y'+y^(2)+1=0

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y" "=" "x" "s in" "x : x yprime=y+xsqrt(x^2-y^2)(x!=0 andx" ">" "y" "or" "x" "<" "" "y )

Verify that the given functions (explicit or implicit) is a solution of the corresponding differential equation: y=sqrt(a^(2)-x^(2))x in(-x,a)vdotsx+y(dy)/(dx)=0(y!=0)

Verify that the given function (explicit of implicit ) is a solution of the corresponding differential equation : (ii) x+y=tan^(-1)y, y^(2)y'+y^(2)+1=0 .