Question

find the orthogonal trajectories of the family of curve where cy square =xcube are orthogonal constant​

Answer 1

Answer:

Then solve the new equation.

So, this is what I have:

The first step is to differentiate with respect to x so find dydx.

dydxx2+dydx2y22x+dydx⋅4ydydx=dydxk2=0=−x2y

Now, the second step is to do the negative recipricol.

dydx=2yx

The third step is to solve the newly formed differential equation.

dy12y∫12ydylny2lnylnyy=1xdx=∫1xdx=lnx+C=2lnx+C=lnx2+C=Ax2

In this case, A=eC. Are my steps correct?