I really hope this isn't a duplicate, today I was answering this question and was to lazy to solve the quadratic equation on my own and so just asked mathematica to give me the solution of the differential equation, but with the student version of mathematica (9.0.1.0)
DSolve[{y'[t] == 1/(1 + Abs[y[t]]) , y[4] == 2}, y[t], t]
and
DSolve[y'[t] == 1/(1 + Abs[y[t]]) && y[4] == 2, y[t], t]
say that there is no solution to this differential equation (the out is {}
),
but with Peano (indeed global Picard-Lindelöf is fulfilled) there must be a solution, which indeed can be calculated. Someone in the chat told me that in Mathematica Version 10.1 a solution to this ode is given.
Abs[ ]
. If you get a monotonous increasing function you'll never need the Abs $\endgroup$Abs[y[t]]
you trySqrt[y[t]^2]
. $\endgroup$y
is real). $\endgroup$