20.10.7 problem Problem 20

Internal problem ID [3779]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.8, A Differential Equation with Nonconstant Coefficients. page 567
Problem number : Problem 20
Date solved : Tuesday, March 04, 2025 at 05:16:29 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=\frac {x^{2}}{\ln \left (x \right )} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x) = x^2/ln(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 24

ode=x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x]==x^2/Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^2 (\log (x) (\log (\log (x))-1+2 c_2)+c_1) \]

✓ Sympy. Time used: 0.279 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x**2/log(x) - 3*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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