87.16.12 problem 12

Internal problem ID [23581]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 119
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:43:09 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+4 x y^{\prime }-10 y&=x \ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=x^2*diff(diff(y(x),x),x)+4*x*diff(y(x),x)-10*y(x) = x*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{5}}+c_1 \,x^{2}-\frac {x \ln \left (x \right )}{6}-\frac {5 x}{36} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 29

ode=x^2*D[y[x],{x,2}]+4*x*D[y[x],x]-10*y[x]==x*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^5}+c_2 x^2-\frac {1}{36} x (6 \log (x)+5) \end{align*}

✓ Sympy. Time used: 0.188 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*log(x) + 4*x*Derivative(y(x), x) - 10*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} + \frac {x^{6} \left (C_{2} x - 6 \log {\left (x \right )} - 5\right )}{36}}{x^{5}} \]