60.3.302 problem 1308

Internal problem ID [11312]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1308
Date solved : Monday, January 27, 2025 at 11:11:07 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{3} y^{\prime \prime }-x^{2} y^{\prime }+y x -\ln \left (x \right )^{3}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 40

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

\[ y = \frac {2 \ln \left (x \right )^{3}+6 \ln \left (x \right )^{2}+\left (8 c_{1} x^{2}+9\right ) \ln \left (x \right )+8 c_{2} x^{2}+6}{8 x} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 41

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

\[ y(x)\to \frac {2 \log ^3(x)+6 \log ^2(x)+9 \log (x)+6}{8 x}+c_1 x+c_2 x \log (x) \]