88.21.7 problem 7

Internal problem ID [24157]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 149
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:00:17 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=6 \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; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 24

ode=x^2*D[y[x],{x,2}]-3*x*D[y[x],{x,1}]+4*y[x]==6; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 19

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

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