60.3.434 problem 1440

Internal problem ID [11444]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1440
Date solved : Monday, January 27, 2025 at 11:22:05 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 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 \left (x \right ) \phi ^{\prime \prime }\left (x \right )\right ) y}{\phi ^{\prime }\left (x \right )+\phi \left (x \right )^{2}} \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],{x,2}] == -((D[y[x],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