60.3.170 problem 1174

Internal problem ID [11180]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1174
Date solved : Monday, January 27, 2025 at 10:47:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }+2 y-x^{5} \ln \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve(x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x)-x^5*ln(x)=0,y(x), singsol=all)
 

\[ y = \frac {\ln \left (x \right ) x^{5}}{12}-\frac {7 x^{5}}{144}+c_{2} x^{2}+c_{1} x \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 32

DSolve[-(x^5*Log[x]) + 2*y[x] - 2*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {7 x^5}{144}+\frac {1}{12} x^5 \log (x)+c_2 x^2+c_1 x \]