Nice to have something to solve while waiting for coeffee.
Manipulate[
eq = \[Epsilon]\[Epsilon] y''[x] + 2 y'[x] + y[x]^3 == 0;
ic = {y[0] == ic0, y[1] == ic1};
sol = First@NDSolve[Flatten[{eq, ic}], y[x], {x, 0, to}];
Plot[y[x] /. sol, {x, 0, to},
Frame -> True,
PlotRange -> All,
ImagePadding -> 50,
FrameLabel -> {
{y[x], None},
{x,
Style[Row[{"solution to ", \[Epsilon] y''[x] + 2 y'[x] +y[x]^3 == 0}], 12]
}
},
GridLines -> Automatic,
GridLinesStyle -> Directive[LightGray, Thickness[.001]]
],
{{\[Epsilon]\[Epsilon], 1, \[Epsilon]}, 0, 1, .01, ImageSize -> Tiny,
Appearance -> "Labeled"},
{{to, 2, "to?"}, 2, 10, .01, ImageSize -> Tiny,
Appearance -> "Labeled"},
{{ic0, 0, "y(0)"}, 0, 1, .01, ImageSize -> Tiny,
Appearance -> "Labeled"},
{{ic1, 0.5, "y(1)"}, 0, 1, .01, ImageSize -> Tiny,
Appearance -> "Labeled"}
]
DSolve
? If you elaborate on that, I (or someone else) can give you an answer that helps you understand how to use it. $\endgroup$sol = First@NDSolve
. What issol
? How do I use it? $\endgroup$