Internal problem ID [8638]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1058.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-x^{2} \left (x +1\right ) y^{\prime }+x \left (x^{4}-2\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.112 (sec). Leaf size: 35
dsolve(diff(diff(y(x),x),x)-x^2*(x+1)*diff(y(x),x)+x*(x^4-2)*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\frac {x^{3}}{3}}+c_{2} {\mathrm e}^{\frac {x^{3}}{3}} \left (\int {\mathrm e}^{\frac {1}{4} x^{4}-\frac {1}{3} x^{3}}d x \right ) \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 44
DSolve[x*(-2 + x^4)*y[x] - x^2*(1 + x)*y'[x] + y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {x^3}{3}} \left (c_2 \int _1^xe^{\frac {1}{12} K[1]^3 (3 K[1]-4)}dK[1]+c_1\right ) \\ \end{align*}