I am trying to solve numerically the following equation $$y'' = xy + y^3$$ I know that for $x<0$ it can be approximately described by $y = \sqrt{-x}$. So I tried to solve it in MATLAB and mathematica with initial conditions $y(-5) = \sqrt{5},~y'(-5) = -1/(2\sqrt{5})$ but both programs failed to solve it properly. After certain iteration the step size became smaller than solver limit. Any suggestions how it can be solved?
2026-02-24 05:32:51.1771911171
Airy-like equation with non-linear term
61 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in NUMERICAL-METHODS
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