60.3.179 problem 1183

Internal problem ID [11189]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1183
Date solved : Monday, January 27, 2025 at 10:48:14 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }-5 y-x^{2} \ln \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)-5*y(x)-x^2*ln(x)=0,y(x), singsol=all)
 

\[ y = c_{2} x^{5}+\frac {c_{1}}{x}-\frac {\ln \left (x \right ) x^{2}}{9} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 27

DSolve[-(x^2*Log[x]) - 5*y[x] - 3*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^5-\frac {1}{9} x^2 \log (x)+\frac {c_1}{x} \]