60.3.304 problem 1310

Internal problem ID [11314]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1310
Date solved : Monday, January 27, 2025 at 11:11:10 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime }+3 x^{2} y^{\prime }+y x -1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(x^3*diff(diff(y(x),x),x)+3*x^2*diff(y(x),x)+x*y(x)-1=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 27

DSolve[-1 + x*y[x] + 3*x^2*D[y[x],x] + x^3*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

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