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I have two problem with which I am stuck:

1- Given the family of curves y=1/(x+C)..

Find the family of orthogonal trajectories

For this problem, I took the first derivative of y---> y'=-1/(x+C)^2. from here, I cannot find the value of C since (x+C)^2=-1/y' which is impossible.

What can I do here?

2- The pairs {x^2+x,x^2} and {x,x+2x^2} ( found by the Wronskian) are base solutions of the equation y''+p(x)y'+q(x)y=0.

Give the general solution of the equation.

Here I dont even know how to start.

Thank you

B

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# 2 problems

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