4.47 problem 1495

Internal problem ID [9822]

Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1495.
ODE order: 3.
ODE degree: 1.

CAS Maple gives this as type [[_3rd_order, _missing_y]]

\[ \boxed {x^{2} y^{\prime \prime \prime }+6 y^{\prime \prime } x +6 y^{\prime }=0} \]

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 16

dsolve(x^2*diff(diff(diff(y(x),x),x),x)+6*x*diff(diff(y(x),x),x)+6*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} +\frac {c_{2}}{x^{2}}+\frac {c_{3}}{x} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 24

DSolve[6*y'[x] + 6*x*y''[x] + x^2*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to -\frac {c_1}{2 x^2}-\frac {c_2}{x}+c_3 \]