Internal problem ID [5267]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 3. Linear equations with variable coefficients. Page 130
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+3 x^{2} y^{\prime }-x y=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: 24
Order:=6; dsolve(diff(y(x),x$2)+3*x^2*diff(y(x),x)-x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1+\frac {x^{3}}{6}\right ) y \relax (0)+\left (x -\frac {1}{6} x^{4}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 28
AsymptoticDSolveValue[y''[x]+3*x^2*y'[x]-x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_2 \left (x-\frac {x^4}{6}\right )+c_1 \left (\frac {x^3}{6}+1\right ) \]