Given the family of curvesOriginally Posted bybraddy

,

rearrange to give:

and differentiate:

or:

.

So now we know that the slope of any curve of the family that passes

through is . So the slope of a curve orthogonal to a member

of the family passing through is . So a curve in the orthoganal family

satisfies the ODE:

Which has solutions:

Which is the required orthogonal family.

RonL