hello,
i would please like your thoughts on the following:
..............(y/5)-1,... y>=0
dy/dx = ........................,y(0)=2, y(x) in C_0[0,inf)
..............(-y/5)-1,... y<0
i am inclined to say this is an initial value problem becuase its to first order and the single condition is (obviously) defined at one (and the same) point, however the initilal condition is only valid for the first equation y'-y/5 -1 so that makes me think twice...
thanks
There is only one equation: y= f(x,y) where x is piecewise defined. The initial condition applies to both pieces. Solve y'= y/5- 1 with y(0)= 2 and then solve y'= -y/5- 1 with y(0)= 2. Because the initial condition occurs at the "break point", x= 0, between the two pieces, the solution will be continuous there.