Internal problem ID [6454]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 17.
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 }+x y^{\prime }-4 y-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 18
dsolve(x^2*diff(diff(y(x),x),x)+x*diff(y(x),x)-4*y(x) = x,y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+\frac {c_{1}}{x^{2}}-\frac {x}{3} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 23
DSolve[x^2*y''[x]+x*y'[x]-4*y[x] == x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x^2+\frac {c_1}{x^2}-\frac {x}{3} \\ \end{align*}