Internal problem ID [9456]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1126.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x +\left (2 a \,x^{3}-1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(x*diff(y(x),x$2)+(2*a*x^3-1)*diff(y(x),x)+(a^2*x^3+a)*x^2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-\frac {x^{3} a}{3}} \left (c_{2} x^{2}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 30
DSolve[x*y''[x]+(2*a*x^3-1)*y'[x]+(a^2*x^3+a)*x^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{-\frac {a x^3}{3}} \left (c_2 x^2+2 c_1\right ) \]