60.3.274 problem 1279

Internal problem ID [11284]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1279
Date solved : Monday, January 27, 2025 at 11:05:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 x^{2} y^{\prime \prime }+5 x y^{\prime }-y-\ln \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 32

dsolve(4*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)-y(x)-ln(x)=0,y(x), singsol=all)
 

\[ y = x^{-\frac {1}{8}+\frac {\sqrt {17}}{8}} c_{2} +x^{-\frac {1}{8}-\frac {\sqrt {17}}{8}} c_{1} -\ln \left (x \right )-1 \]

✓ Solution by Mathematica

Time used: 0.125 (sec). Leaf size: 45

DSolve[-Log[x] - y[x] + 5*x*D[y[x],x] + 4*x^2*D[y[x],{x,2}] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^{\frac {1}{8} \left (\sqrt {17}-1\right )}+c_1 x^{-\frac {1}{8}-\frac {\sqrt {17}}{8}}-\log (x)-1 \]