(x^(2)+y^(2))(dy)/(dx)=2xy

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

The first integral of (dy)/(dx)((d^(2)y)/(dx^(2)))-x^(2)y((dy)/(dx))=xy^(2) will be

y^(2)+x^(2)(dy)/(dx)=xy(dy)/(dx)

y^(2)-x^(2) (dy)/(dx) = xy(dy)/(dx)

Solve y^(2)+x^(2)(dy)/(dx)=xy(dy)/(dx)

Solve the following differential equations. (x^(2)+y^(2))dy=2xy dx

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

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