dy/dx=-2y/x
Solve y(-1)=2
y=2/x^2"
Find the isoclines of this DE?

Question

dy/dx=-2y/x
Solve y(-1)=2
y=2/x^2"
Find the isoclines of this DE?

anonymous · Answer

there are infinite number of isoclines :)) but we do need to sketch some of them to have a direction field so let's do that...
so if dy/dx=0 then isocline y=0, if dy/dx=-2 we have y=x, if dy/dx=-4 we have y=2x
if dy/dx=2 we have isocline y=-x. if dy/dx=4 we have isocline y=-2x.. so let's now.
notice that y=0 will also be a solution since in any point it will be tangential to a line element in the direction field...

anonymous · Answer

although i'm not sure how you're getting all of that.

anonymous · Answer

would it help if I draw the direction field itself? :)).. I know at first this may seem confusing to some but after mastering this thing is a very nice thing to happen. After all, there are lots of worldwide phenomenons which can be modelled using differential equations...

anonymous · Answer

that would be helpful if you could!