29.7.17 problem 20

Internal problem ID [7334]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 04:29:09 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=6 x^{2} \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x) = 6*ln(x)*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2} \left (c_2 +c_1 \ln \left (x \right )+\ln \left (x \right )^{3}\right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 22

ode=x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x]==6*x^2*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2 \left (\log ^3(x)+2 c_2 \log (x)+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.176 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x**2*log(x) + x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (C_{1} + C_{2} \log {\left (x \right )} + \log {\left (x \right )}^{3}\right ) \]