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Solve in the series eqation d2y/dx2+x2y=0

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  \frac{d^2y}{dx^2}=-x^2y
Bring y to LHS and x to RHS:     \frac{d^2y}{y}=-x^2dx^2
Integrate on both sides: wrt y on LHS and x on RHS. 
 \int \frac{d^2y}{y}=\int -x^2dx^2\\\Rightarrow \int \frac{dy}{y}*dy=\int (-x^2dx)dx\\\Rightarrow (lny)dy=(-\frac{1}{3}x^3)dx
 Integrate again we get:     ylny-y=-\frac{1}{12}x^4

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avinash.dongre

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