Internal problem ID [9514]
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]]
\[ \boxed {x^{2} y^{\prime \prime }-4 y^{\prime } x +6 y=x^{4}-x^{2}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
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)
\[ y \left (x \right ) = \frac {x^{2} \left (2 x c_{2} +x^{2}+2 \ln \left (x \right )+2 c_{1} +2\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.018 (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]
\[ y(x)\to \frac {1}{2} x^2 \left (x^2+2 \log (x)+2 c_2 x+2+2 c_1\right ) \]