Internal problem ID [9053]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1474.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+3 f \relax (x ) y^{\prime \prime }+\left (f^{\prime }\relax (x )+2 f \relax (x )^{2}+4 g \relax (x )\right ) y^{\prime }+\left (4 f \relax (x ) g \relax (x )+2 g^{\prime }\relax (x )\right ) y=0} \end {gather*}
✗ Solution by Maple
dsolve(diff(diff(diff(y(x),x),x),x)+3*f(x)*diff(diff(y(x),x),x)+(diff(f(x),x)+2*f(x)^2+4*g(x))*diff(y(x),x)+(4*f(x)*g(x)+2*diff(g(x),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]*(4*f[x]*g[x] + 2*Derivative[1][g][x]) + (2*f[x]^2 + 4*g[x] + Derivative[1][f][x])*y'[x] + 3*f[x]*y''[x] + Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved