54.3.263 problem 1279

Internal problem ID [12558]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1279
Date solved : Wednesday, October 01, 2025 at 02:06:40 AM
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*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 32

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

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

✓ Mathematica. Time used: 0.08 (sec). Leaf size: 45

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

\begin{align*} 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 \end{align*}

✓ Sympy. Time used: 0.184 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) - y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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