In classical mechanics solve in series the equation d2y/dx2+x2y=0
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d² y / d x² = - x² y
d² y / y = -x² d x²
integrate
log y d y +c1 = - 1/3 x³ dx + c2
integrate
y logy - y + c1 y = -1/12 x^4 + c2 x + c3
d² y / d x² = - x² y
d² y / y = -x² d x²
integrate
log y d y +c1 = - 1/3 x³ dx + c2
integrate
y logy - y + c1 y = -1/12 x^4 + c2 x + c3
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