Internal problem ID [4719]
Book: A treatise on Differential Equations by A. R. Forsyth. 6th edition. 1929. Macmillan Co. ltd. New
York, reprinted 1956
Section: Chapter VI. Note I. Integration of linear equations in series by the method of Frobenius. page
243
Problem number: Ex. 6(i), page 257.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (1+x \right ) y^{\prime \prime }-\left (1+2 x \right ) \left (x y^{\prime }-y\right )=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.019 (sec). Leaf size: 35
Order:=6; dsolve(x^2*(1+x)*diff(y(x),x$2)-(1+2*x)*(x*diff(y(x),x)-y(x))=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (\left (\ln \relax (x ) c_{2}+c_{1}\right ) \left (1+\mathrm {O}\left (x^{6}\right )\right )+\left (x +\mathrm {O}\left (x^{6}\right )\right ) c_{2}\right ) x \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 2760
AsymptoticDSolveValue[x^2*(1+x)*y''[x]-(1+2*x)*(x*y'[x]+y[x])==0,y[x],{x,0,5}]
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