Internal problem ID [9071]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1494.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {x^{2} y^{\prime \prime \prime }+5 y^{\prime \prime } x +4 y^{\prime }-\ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve(x^2*diff(diff(diff(y(x),x),x),x)+5*x*diff(diff(y(x),x),x)+4*diff(y(x),x)-ln(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +\frac {c_{2} \ln \left (x \right )}{x}+\frac {c_{3}}{x}+\frac {x \left (-2+\ln \left (x \right )\right )}{4} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 43
DSolve[-Log[x] + 4*y'[x] + 5*x*y''[x] + x^2*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\left (x^2-8 c_2\right ) \log (x)-2 \left (x^2-2 c_3 x+2 c_1+4 c_2\right )}{4 x} \\ \end{align*}