Internal problem ID [9018]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1439.
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 {\phi ^{\prime }\relax (x ) y^{\prime }}{\phi \relax (x )-\phi \relax (a )}+\frac {\left (-n \left (n +1\right ) \left (\phi \relax (x )-\phi \relax (a )\right )^{2}+D^{\relax (2)}\left (\phi \right )\relax (a )\right ) y}{\phi \relax (x )-\phi \relax (a )}=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x) = diff(phi(x),x)/(phi(x)-phi(a))*diff(y(x),x)-(-n*(n+1)*(phi(x)-phi(a))^2+(D@@2)(phi)(a))/(phi(x)-phi(a))*y(x),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == (Derivative[1][phi][x]*y'[x])/(-phi[a] + phi[x]) - (y[x]*(-(n*(1 + n)*(-phi[a] + phi[x])^2) + Derivative[2][phi][a]))/(-phi[a] + phi[x]),y[x],x,IncludeSingularSolutions -> True]
Not solved