Internal problem ID [4531]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 8, Series solutions of differential equations. Section 8.4. page 449
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 x y^{\prime }+3 y-x^{2}=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 36
Order:=6; dsolve(diff(y(x),x$2)-2*x*diff(y(x),x)+3*y(x)=x^2,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {3}{2} x^{2}-\frac {1}{8} x^{4}\right ) y \relax (0)+\left (x -\frac {1}{6} x^{3}-\frac {1}{40} x^{5}\right ) D\relax (y )\relax (0)+\frac {x^{4}}{12}+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 49
AsymptoticDSolveValue[y''[x]-2*x*y'[x]+3*y[x]==x^2,y[x],{x,0,5}]
\[ y(x)\to \frac {x^4}{12}+c_2 \left (-\frac {x^5}{40}-\frac {x^3}{6}+x\right )+c_1 \left (-\frac {x^4}{8}-\frac {3 x^2}{2}+1\right ) \]