Ordinary Differential Equations/Separable 4

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Existence problems[edit]

1) f(x,y) has no discontinuities, so a solution exists. has no discontinuities, so the solution is unique.

2) f(x,y) is not defined for the point (-1,10) because ln(x) is not defined. So no solution exists.

3) f(x,y) has discontinuities at y=1 and -1, but not at 0 so a solution exists. has no discontinuities at (0,16) so the solution is unique.

4) f(x,y) has discontinuities at y<0, but not at 1 so a solution exists. is discontinuous at 1, so the solution is not unique

5) f(x,y) has discontinuities at -3 and -4, but not at 0 so a solution exists. has no discontinuities at (5,9) so the solution is unique.

6) f(x,y) has a discontinuity at x=5, so no solution exists.

Separable equations[edit]

7)


8)


9)


10)


11)


12)

Initial value problems[edit]

13)


14)