Internal problem ID [8706]
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]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }+\left (2 x^{3} a -1\right ) y^{\prime }+\left (a^{2} x^{3}+a \right ) x^{2} y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(x*diff(diff(y(x),x),x)+(2*a*x^3-1)*diff(y(x),x)+(a^2*x^3+a)*x^2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{-\frac {x^{3} a}{3}}+c_{2} {\mathrm e}^{-\frac {x^{3} a}{3}} x^{2} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a + a^2*x^3)*y[x] + (-1 + 2*a*x^3)*y'[x] + x*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved