18.2.10 problem Problem 15.21

Internal problem ID [3493]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page 523
Problem number : Problem 15.21
Date solved : Sunday, March 30, 2025 at 01:44:53 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=x \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

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

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{2} x \left (\log ^2(x)+2 c_2 \log (x)+2 c_1\right ) \]

✓ Sympy. Time used: 0.228 (sec). Leaf size: 17

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

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