85.64.10 problem 1 (j)

Internal problem ID [22877]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 213
Problem number : 1 (j)
Date solved : Thursday, October 02, 2025 at 09:16:08 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }&=5 \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x) = 5*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1 \,x^{3}}{3}-\frac {5 \ln \left (x \right )^{2}}{6}-\frac {5 \ln \left (x \right )}{9}+c_2 \]

✓ Mathematica. Time used: 0.029 (sec). Leaf size: 31

ode=x^2*D[y[x],{x,2}]-2*x*D[y[x],x]==5*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1 x^3}{3}-\frac {5 \log ^2(x)}{6}-\frac {5 \log (x)}{9}+c_2 \end{align*}

✓ Sympy. Time used: 0.142 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 2*x*Derivative(y(x), x) - 5*log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} x^{3} - \frac {5 \log {\left (x \right )}^{2}}{6} - \frac {5 \log {\left (x \right )}}{9} \]