# Higher order differential equation

Someone can help me? I search an algorithm or an reference which can help me to solve third order differential equation of the form \begin{equation*} a_3(x)y^{(3)}+a_2(x)y^{(2)}+a_1(x)y^{(1)}+a_0(x)y=0 \end{equation*} where $a_0,a_1,a_2,a_3$ are polynomial coeficients. I have tried by doing the reduction of the order but nothing. Thanks

• Try using series method. Set $y= \sum_{n=0}^\infty a_n x^n$ and you will reduce the problem to a recurrence relation for coefficients $a_n$ – user26977 Aug 14 '16 at 15:59