60.4.81 problem 1531

Internal problem ID [11532]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1531
Date solved : Monday, January 27, 2025 at 11:23:15 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} f^{\prime }\left (x \right ) y^{\prime \prime }+f \left (x \right ) y^{\prime \prime \prime }+g^{\prime }\left (x \right ) y^{\prime }+g \left (x \right ) y^{\prime \prime }+h^{\prime }\left (x \right ) y+h \left (x \right ) y^{\prime }+A \left (x \right ) \left (f \left (x \right ) y^{\prime \prime }+g \left (x \right ) y^{\prime }+h \left (x \right ) y\right )&=0 \end{align*}

✗ Solution by Maple

dsolve(diff(f(x),x)*diff(diff(y(x),x),x)+f(x)*diff(diff(diff(y(x),x),x),x)+diff(g(x),x)*diff(y(x),x)+g(x)*diff(diff(y(x),x),x)+diff(h(x),x)*y(x)+h(x)*diff(y(x),x)+A(x)*(f(x)*diff(diff(y(x),x),x)+g(x)*diff(y(x),x)+h(x)*y(x))=0,y(x), singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[y[x]*Derivative[1][h][x] + h[x]*D[y[x],x] + Derivative[1][g][x]*D[y[x],x] + g[x]*D[y[x],{x,2}] + Derivative[1][f][x]*D[y[x],{x,2}] + A[x]*(h[x]*y[x] + g[x]*D[y[x],x] + f[x]*D[y[x],{x,2}]) + f[x]*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

Not solved