Internal problem ID [9768]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1440.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+\frac {\left (\phi \left (x^{3}\right )-\phi \left (x \right ) \phi ^{\prime }\left (x \right )-\phi ^{\prime \prime }\left (x \right )\right ) y^{\prime }}{\phi ^{\prime }\left (x \right )+\phi \left (x \right )^{2}}+\frac {\left ({\phi ^{\prime }\left (x \right )}^{2}-\phi \left (x \right )^{2} \phi ^{\prime }\left (x \right )-\phi ^{\prime \prime }\left (x \right ) \phi \left (x \right )\right ) y}{\phi ^{\prime }\left (x \right )+\phi \left (x \right )^{2}}=0} \]
✗ Solution by Maple
dsolve(diff(diff(y(x),x),x) = -(phi(x^3)-phi(x)*diff(phi(x),x)-diff(diff(phi(x),x),x))/(diff(phi(x),x)+phi(x)^2)*diff(y(x),x)-(diff(phi(x),x)^2-phi(x)^2*diff(phi(x),x)-phi(x)*diff(diff(phi(x),x),x))/(diff(phi(x),x)+phi(x)^2)*y(x),y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x] == -((y'[x]*(phi[x^3] - phi[x]*Derivative[1][phi][x] - Derivative[2][phi][x]))/(phi[x]^2 + Derivative[1][phi][x])) - (y[x]*(-(phi[x]^2*Derivative[1][phi][x]) + Derivative[1][phi][x]^2 - phi[x]*Derivative[2][phi][x]))/(phi[x]^2 + Derivative[1][phi][x]),y[x],x,IncludeSingularSolutions -> True]
Not solved