# Integrated Solution Graphics [closed]

I want to draw this nonlinear differantial equation' graphic with other solving equation (in same graphic).

ϵ y''[x] + y'[x] + y[x]^2 == 0, y == 0, y == 1/2

y^c = 1/(x +
1) - (1 + 2 x) E^(-(
x/ϵ)) + ϵ {2/(x + 1)^2 Log[2/(
x + 1)] + (1/2 - 2 Log) E^(-(x/ϵ)) -
1/2 E^(-((2 x)/ϵ))}


I got nonlinear differantial equation' numerical solution with this form.

ϵ = 0.1;
functions = NDSolveValue[{ϵ y''[x] + y'[x] + y[x]^2 == 0, y == 0,
y == 1/2}, {y, x}, {x, 0, 1}];

Plot[Evaluate@Through@functions@x, {x, 0, 1}] ## 1 Answer

ϵ = 0.1;

func = NDSolveValue[{ϵ y''[x] + y'[x] + y[x]^2 == 0, y == 0, y == 1/2},
y, {x, 0, 1}]

y2[x_] := 1/(x + 1) - (1 + 2 x) E^(-(x/ϵ)) + ϵ (2/(x + 1)^2 Log[2/(x + 1)]
+ (1/2 - 2 Log) E^(-(x/ϵ)) - 1/2 E^(-((2 x)/ϵ)))


You can display both functions inside one plot using

Plot[{func[x], y2[x]}, {x, 0, 1}] or

p1 = Plot[func[x], {x, 0, 1}];
p2 = Plot[y2[x], {x, 0, 1}];
Show[p1, p2] • @GenceDeveci What version of Mathematica are you using? – Karsten 7. Mar 28 '15 at 11:57
• I'm using the Mathematica 9.0 ( "c" is not number it is only constant as a character) – Gence Deveci Mar 28 '15 at 12:06