Internal problem ID [253]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number: 58.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y-x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 23
dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=x^3,y(x), singsol=all)
\[ y \relax (x ) = x^{3} c_{2}+c_{1} x^{2}+x^{3} \left (\ln \relax (x )-1\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 22
DSolve[x^2*y''[x]-4*x*y'[x]+6*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^2 (x \log (x)+(-1+c_2) x+c_1) \\ \end{align*}