Verify that the given functions ( explicit or implicit ) is a solution of the corresponding differential equation :
`y=sqrt(a^(2)-x^(2))x in(-a,a)`
` x+y(dy)/(dx)=0(yne0)`

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=x^(2)+2x+C:y'-2x-2=0

Verify that the given functions ( explicit or implicit ) is a solution of the corresponding differential equation : y=Ax:xy'=y(xne0)

Verify that the given functions ( explicit or implicit ) is a solution of the corresponding differential equation : y=cosx+C:y'+sinx=0

Verify that the given functions ( explicit or implicit ) is a solution of the corresponding differential equation : xy=logy+K:y'=(y^(2))/(1-xy)(xyne1)

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-cosy=x:(ysiny+cosy+x) y'=y .

Verify that the given functions ( explicit or implicit ) is a solution of the corresponding differential equation : y=xsinx : xy'=y+xsqrt(x^(2)-y^(2)) (xne0"and"x lt y"or"x gt -y)

y = sqrt(a^(2) - x^(2)) x ne (-a, a) : x + y (dy)/(dx) = 0(y ne 0)

For each of the exercises given below, verify that the given function ( implicit or explicit ) is a solution of the corresponding differential equation. x^(2)=2y^(2)logy:(x^(2)+y^(2))(dy)/(dx)-xy=0