Internal problem ID [9110]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1531.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {f^{\prime }\relax (x ) y^{\prime \prime }+f \relax (x ) y^{\prime \prime \prime }+g^{\prime }\relax (x ) y^{\prime }+g \relax (x ) y^{\prime \prime }+h^{\prime }\relax (x ) y+h \relax (x ) y^{\prime }+A \relax (x ) \left (f \relax (x ) y^{\prime \prime }+g \relax (x ) y^{\prime }+h \relax (x ) y\right )=0} \end {gather*}
✗ 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: 0.0 (sec). Leaf size: 0
DSolve[y[x]*Derivative[1][h][x] + h[x]*y'[x] + Derivative[1][g][x]*y'[x] + g[x]*y''[x] + Derivative[1][f][x]*y''[x] + A[x]*(h[x]*y[x] + g[x]*y'[x] + f[x]*y''[x]) + f[x]*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved