4.10.17 problem 17

Internal problem ID [1349]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 04:32:57 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 20

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);
 

\[ y = x^{2} \left (c_2 +c_1 \ln \left (x \right )+\frac {\ln \left (x \right )^{3}}{6}\right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 27

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]
 

\begin{align*} y(x)&\to \frac {1}{6} x^2 \left (\log ^3(x)+12 c_2 \log (x)+6 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.193 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-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)
 

\[ y{\left (x \right )} = x^{2} \left (C_{1} + C_{2} \log {\left (x \right )} + \frac {\log {\left (x \right )}^{3}}{6}\right ) \]