28.2.67 problem 67

Internal problem ID [4510]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 67
Date solved : Sunday, March 30, 2025 at 03:24:27 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+5 y&=\frac {5 \ln \left (x \right )}{x^{2}} \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=x^2*diff(diff(y(x),x),x)+3*x*diff(y(x),x)+5*y(x) = 5/x^2*ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5 \sin \left (2 \ln \left (x \right )\right ) c_2 x +5 \cos \left (2 \ln \left (x \right )\right ) c_1 x +5 \ln \left (x \right )+2}{5 x^{2}} \]

✓ Mathematica. Time used: 0.112 (sec). Leaf size: 38

ode=x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+5*y[x]==5/x^2*Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {5 \log (x)+5 c_2 x \cos (2 \log (x))+5 c_1 x \sin (2 \log (x))+2}{5 x^2} \]

✓ Sympy. Time used: 0.552 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 3*x*Derivative(y(x), x) + 5*y(x) - 5*log(x)/x**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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