Verify that `y=c e^(t a n-1_x)` is a solution of differential equation `(1+x^2)(d^2y)/(dx^2)+(2x-1)(dy)/(dx)=0.`

Verify that y=ce^(tan-1_(z)) is a solution of differential equation (1+x^(2))(d^(2)y)/(dx^(2))+(2x-1)(dy)/(dx)=0

Verify that y=e^(m sin^(-1)x) is a solution of the differential equation (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-m^(2)y=0.

y = log x + c is a solution of the differential equation x(d^(2)y)/(dx^(2)) + (dy)/(dx) = 0

Verify that y=ae^(3x)+be^(-x) is a solution of differential equation (d^2y)/(dx^2)-2(dy)/(dx)-3y=0

Verify that y=ae^(3x)+be^(-x) is a solution of differential equation (d^2y)/(dx^2)-2(dy)/(dx)-3y=0

Verify that y=(c-x)/(1+cx) is a solution of the differential equation (1+x^(2))(dy)/(dx)+(1+y^(2))=0.

Verify that y=e^x(acosx+csinx) is a solution of the differential equation (d^2y)/dx^2-2(dy)/(dx)+2y=0

Verify that the function y = e^(2x) is a solution of the differential equation (d^(2)y)/(dx^(2)) + (dy)/(dx) - 6y = 0