Internal problem ID [4717]
Book: Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill
2014
Section: Chapter 27. Power series solutions of linear DE with variable coefficients. Supplementary
Problems. page 274
Problem number: Problem 27.48.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 x y^{\prime }+y x^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = -1] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 18
Order:=6; dsolve([diff(y(x),x$2)-2*x*diff(y(x),x)+x^2*y(x)=0,y(0) = 1, D(y)(0) = -1],y(x),type='series',x=0);
\[ y \relax (x ) = 1-x -\frac {1}{3} x^{3}-\frac {1}{12} x^{4}-\frac {1}{20} x^{5}+\mathrm {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 29
AsymptoticDSolveValue[{y''[x]-2*x*y'[x]+x^2*y[x]==0,{y[0]==1,y'[0]==-1}},y[x],{x,0,5}]
\[ y(x)\to -\frac {x^5}{20}-\frac {x^4}{12}-\frac {x^3}{3}-x+1 \]