87.18.16 problem 16

Internal problem ID [23657]
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 135
Problem number : 16
Date solved : Thursday, October 02, 2025 at 09:43:55 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+7 x y^{\prime }-3 y&=\frac {\ln \left (x \right )}{x^{2}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=2*x^2*diff(diff(y(x),x),x)+7*x*diff(y(x),x)-3*y(x) = ln(x)/x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_2}{x^{3}}+\sqrt {x}\, c_1 +\frac {-5 \ln \left (x \right )+3}{25 x^{2}} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 33

ode=2*x^2*D[y[x],{x,2}]+7*x*D[y[x],x]-3*y[x]==Log[x]/x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {c_1}{x^3}+\frac {3-5 \log (x)}{25 x^2}+c_2 \sqrt {x} \end{align*}

✓ Sympy. Time used: 0.214 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 7*x*Derivative(y(x), x) - 3*y(x) - log(x)/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} x^{2} + C_{2} x^{\frac {11}{2}} + \frac {x^{3} \left (3 - 5 \log {\left (x \right )}\right )}{25}}{x^{5}} \]