(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the families (x+c1)(x^{2}+y^{2})+x = 0 and (y+c2)(x^{2}+y^{2})-y = 0

2. Relevant equations

For the 2 curves to be orthogonal their slopes should be negative recriprocles.

3. The attempt at a solution

I'm pretty sure that for the first set of curves:

y'(x) = - (2c1 x + 3x^{2}+y[x]^{2}+1)/(2(c1+x)y[x])

and for the second set of curves:

y'(x) = (2x (c2 +y)) / (2c2 y[x] + x^{2}+ 3y[x]^{2}-1)

which are not negative recriprocles of each other.

I'm thinking i went wrong somewhere along the lines of finding the deravitive. if anyone could please help me out i'd really appreciate it.

I used Mathematica to get those answers:

For the first set i factored out the original problem then took the deravitive of that:

D[c1 x^2 + c1 y[x]^2 + x^3 + x y[x]^2 + x, x]

then i used the solve command to solve that for y'[x]

For the second set i factored out the original problem, then took the deravitive of that with respect to x:

D[c2 x^2 + c2 y[x]^2 + x^2 y[x] + y[x]^3 - y[x], x]

Then i used the Solve[] function to solve that for y'[x]

P.S. I'm pretty sure these are supposed to be orthogonal just because there isn't an option for not orthogonal.

Like i said any help would be appreciated.

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# Homework Help: Need help on Orthogonal Trajectories in my Diff. EQ. Class

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