Internal problem ID [8987]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1408.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+\frac {\left (x^{2} \left (\left (x^{2}-\mathit {a1} \right ) \left (x^{2}-\mathit {a2} \right )+\left (x^{2}-\mathit {a2} \right ) \left (x^{2}-\mathit {a3} \right )+\left (x^{2}-\mathit {a3} \right ) \left (x^{2}-\mathit {a1} \right )\right )-\left (x^{2}-\mathit {a1} \right ) \left (x^{2}-\mathit {a2} \right ) \left (x^{2}-\mathit {a3} \right )\right ) y^{\prime }}{x \left (x^{2}-\mathit {a1} \right ) \left (x^{2}-\mathit {a2} \right ) \left (x^{2}-\mathit {a3} \right )}+\frac {\left (A \,x^{2}+B \right ) y}{x \left (x^{2}-\mathit {a1} \right ) \left (x^{2}-\mathit {a2} \right ) \left (x^{2}-\mathit {a3} \right )}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x) = -(x^2*((x^2-a1)*(x^2-a2)+(x^2-a2)*(x^2-a3)+(x^2-a3)*(x^2-a1))-(x^2-a1)*(x^2-a2)*(x^2-a3))/x/(x^2-a1)/(x^2-a2)/(x^2-a3)*diff(y(x),x)-(A*x^2+B)/x/(x^2-a1)/(x^2-a2)/(x^2-a3)*y(x),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == -(((B + A*x^2)*y[x])/(x*(-a1 + x^2)*(-a2 + x^2)*(-a3 + x^2))) - (((a1 - x^2)*(-a2 + x^2)*(-a3 + x^2) + x^2*((-a1 + x^2)*(-a2 + x^2) + (-a1 + x^2)*(-a3 + x^2) + (-a2 + x^2)*(-a3 + x^2)))*y'[x])/(x*(-a1 + x^2)*(-a2 + x^2)*(-a3 + x^2)),y[x],x,IncludeSingularSolutions -> True]
Not solved