# Question:Where does this difference between formal and numeric dsolve come from?

## Question:Where does this difference between formal and numeric dsolve come from?

Maple 2015

Hi,

I have a 2nd order linear ODE that I solved firstly in a formal way.
The plot of the solution contains a "hole" which, in fact, corresponds to the range where the formal solution is not real.
This seemed strange to me as I expected a real solution.
So I solved this ODE numerically and this gave me a real solution.
Could you please explain that to me ?

PS : These results are obtained with Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895

 > restart:
 > with(plots):
 > perturbation := .9*(diff(epsilon(t), t, t)) = (-28.67085587*piecewise(0.2000000000e-1*t < 0.8e-1, 0., 0.2000000000e-1*t < .12, -0.8e-1+0.2000000000e-1*t, 0.2000000000e-1*t < .14, .16-0.2000000000e-1*t, 0.2e-1)-0.7645561571e-1*t-1.548363347)*(diff(epsilon(t), t))-0.7596363e-1*piecewise(0.2000000000e-1*t < 0.8e-1, 0., 0.2000000000e-1*t < .12, -0.8e-1+0.2000000000e-1*t, 0.2000000000e-1*t < .14, .16-0.2000000000e-1*t, 0.2e-1)-0.202569683e-3*t+0.26997403e-1-10.10*epsilon(t)
 (1)
 > Digits:=10: EPS := rhs( dsolve({evalf(perturbation), epsilon(0)=0, D(epsilon)(0)=0}, epsilon(t)) ): # a lengthy expression that involves Kummer's special functions
 > plot(EPS, t=0..10, gridlines=true); Digits:=20: evalf(eval(EPS, t=5)); Digits:=10:
 (2)
 > numsol := dsolve({perturbation, epsilon(0)=0, D(epsilon)(0)=0}, numeric): odeplot(numsol, [t, epsilon(t)], t=0..10, gridlines=true, color=red)
 >