Internal problem ID [8764]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1184.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y-x^{4}+x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 29
dsolve(x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+6*y(x)-x^4+x^2=0,y(x), singsol=all)
\[ y \relax (x ) = x^{3} c_{2}+c_{1} x^{2}+\frac {x^{2} \left (x^{2}+2 \ln \relax (x )+2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 30
DSolve[x^2 - x^4 + 6*y[x] - 4*x*y'[x] + x^2*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} x^2 \left (x^2+2 \log (x)+2 c_2 x+2+2 c_1\right ) \\ \end{align*}