- #1

- 2

- 0

- Homework Statement
- (a) Solve the differential equation:

[x * (dy/dx)^2] - [2y*(dy/dx)] - x = 0

How many integral curves pass through each point of the (x,y) plane (except x = 0)?

why is the solution at each point not unique

(b) The differential equation:

[(dy/dx)^2] + [f(x,y)*(dy/dx)] - 1 = 0

represents a set of curves such that two curves pass through any given point. Show that these curves intersect at right angles at the point. at f = -2y/x verify this property for the point (3,4)

- Relevant Equations
- differential equations

I'm aware that I can introduce the perimeter p = dy/dx

then I can rearrange my equation to make y the subject, then I can show that dp/dx = p/x. However, this only gives me a bunch of quadratic curves for my solution. However given part b I see that two curves are meant to intersect each point and I don't know where I'll get the second set of curves (solutions) from.

for part b honestly I don't even know where to start

then I can rearrange my equation to make y the subject, then I can show that dp/dx = p/x. However, this only gives me a bunch of quadratic curves for my solution. However given part b I see that two curves are meant to intersect each point and I don't know where I'll get the second set of curves (solutions) from.

for part b honestly I don't even know where to start