# Determine the power series solution of the differential equation

I am trying to find a solution how to determine the power series solution of the differential equation using Leibnitz - Maclaurin's method.

$$\frac{d^2 x}{dy^2} +5y \frac{dx}{dy}+x=0$$

boundary conditions being $x(0)=5$ and $\frac{dx}{dy}(0)=3$ when $y=0$

Thanks. Joe

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What have your tried? –  lhf Mar 21 '12 at 23:02

Hint: If you write the solution as $x = \sum_{k=0}^\infty a_k y^k$, the initial conditions give you $a_0$ and $a_1$, and the coefficient of $y^k$ in the left side of the differential equation gives you a recurrence relation involving $a_{k+2}$ and $a_k$.