Question

How to find that cauchy problem had unique solution or infinite solution or no solution?

Answer 1

when
a1/a2≠b1/b2
then, the equation have unique solution

a1/a2=b1/b2≠c1/c2
then,the equation have no solution

a1/a2=b1/b2=c1/c2
then,the equation have infinite solutions.

where equation are in the form of
a1x+b1y=c1
a2x+b2y=c2