Internal problem ID [5456]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 25. Integration in series. Supplemetary problems. Page 205
Problem number: 15.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime } x +y x^{2}=0} \] With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
Order:=6; dsolve(diff(y(x),x$2)-x*diff(y(x),x)+x^2*y(x)=0,y(x),type='series',x=0);
\[ y = \left (1-\frac {x^{4}}{12}\right ) y \left (0\right )+\left (x +\frac {1}{6} x^{3}-\frac {1}{40} x^{5}\right ) y^{\prime }\left (0\right )+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 35
AsymptoticDSolveValue[y''[x]-x*y'[x]+x^2*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (1-\frac {x^4}{12}\right )+c_2 \left (-\frac {x^5}{40}+\frac {x^3}{6}+x\right ) \]