60.3.433 problem 1439

Internal problem ID [11443]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1439
Date solved : Monday, January 27, 2025 at 11:22:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\phi ^{\prime }\left (x \right ) y^{\prime }}{\phi \left (x \right )-\phi \left (a \right )}-\frac {\left (-n \left (n +1\right ) \left (\phi \left (x \right )-\phi \left (a \right )\right )^{2}+D^{\left (2\right )}\left (\phi \right )\left (a \right )\right ) y}{\phi \left (x \right )-\phi \left (a \right )} \end{align*}

✗ 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: 0.000 (sec). Leaf size: 0

DSolve[D[y[x],{x,2}] == (Derivative[1][phi][x]*D[y[x],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