Internal problem ID [9090]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1511.
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 } x^{3}+3 x^{2} y^{\prime \prime }-2 y^{\prime } x +2 y-6 x^{3} \left (x -1\right ) \ln \relax (x )+x^{3} \left (x +8\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 37
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x)-6*x^3*(x-1)*ln(x)+x^3*(x+8)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3} \left (50 x \ln \relax (x )-135 \ln \relax (x )-50 x -18\right )}{450}+x c_{1}+\frac {c_{2}}{x^{2}}+c_{3} x \ln \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.036 (sec). Leaf size: 52
DSolve[x^3*(8 + x) - 6*(-1 + x)*x^3*Log[x] + 2*y[x] - 2*x*y'[x] + 3*x^2*y''[x] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x^4}{9}-\frac {x^3}{25}+\frac {c_1}{x^2}+\left (\frac {x^4}{9}-\frac {3 x^3}{10}+c_3 x\right ) \log (x)+c_2 x \\ \end{align*}