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d2 y / d x2 = - x2
y

Bring y to LHS and x to RHS: d2 y / y = - x2 d x2

Integrate on both sides: wrt y on LHS and x on RHS.

dx2 is dx * dx and d2y is dy * dy.

ln y dy = - 1/3 x3 dx

Integrate again: y ln y – y = - 1/12 x4

Bring y to LHS and x to RHS: d2 y / y = - x2 d x2

Integrate on both sides: wrt y on LHS and x on RHS.

dx2 is dx * dx and d2y is dy * dy.

ln y dy = - 1/3 x3 dx

Integrate again: y ln y – y = - 1/12 x4