Internal problem ID [6453]
Book: Own collection of miscellaneous problems
Section: section 3.0
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{4} y^{\prime \prime }+y^{\prime } x^{3}-4 y x^{2}-x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 20
dsolve(x^4*diff(y(x),x$2)+x^3*diff(y(x),x)-4*x^2*y(x)=x,y(x), singsol=all)
\[ y \relax (x ) = x^{2} c_{2}+\frac {c_{1}}{x^{2}}-\frac {1}{3 x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 25
DSolve[x^4*y''[x]+x^3*y'[x]-4*x^2*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 x^2+\frac {c_1}{x^2}-\frac {1}{3 x} \\ \end{align*}