60.4.47 problem 1495

Internal problem ID [11498]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1495
Date solved : Monday, January 27, 2025 at 11:22:42 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime \prime }+6 x y^{\prime \prime }+6 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = c_{1} +\frac {c_{2}}{x}+\frac {c_3}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 23

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

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