Internal problem ID [5459]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 26. Integration in series (singular points). Supplemetary problems. Page
218
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {2 \left (x^{3}+x^{2}\right ) y^{\prime \prime }-\left (-3 x^{2}+x \right ) y^{\prime }+y=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
Order:=6; dsolve(2*(x^2+x^3)*diff(y(x),x$2)-(x-3*x^2)*diff(y(x),x)+y(x)=0,y(x),type='series',x=0);
\[ y \left (x \right ) = \left (-x^{5}+x^{4}-x^{3}+x^{2}-x +1\right ) \left (c_{1} \sqrt {x}+c_{2} x \right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 58
AsymptoticDSolveValue[2*(x^2+x^3)*y''[x]-(x-3*x^2)*y'[x]+y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 x \left (-x^5+x^4-x^3+x^2-x+1\right )+c_2 \sqrt {x} \left (-x^5+x^4-x^3+x^2-x+1\right ) \]