82.39.14 problem Ex. 14

Internal problem ID [18875]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VII. Linear equations with variable coefficients. End of chapter problems at page 91
Problem number : Ex. 14
Date solved : Monday, March 31, 2025 at 06:17:48 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+y&=\frac {\ln \left (x \right ) \sin \left (\ln \left (x \right )\right )+1}{x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 55

ode:=x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+y(x) = (ln(x)*sin(ln(x))+1)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {22326 x^{3} x^{-\sqrt {3}} c_1 +22326 x^{3} x^{\sqrt {3}} c_2 +\left (1146+162 i+\left (1098+915 i\right ) \ln \left (x \right )\right ) x^{-i}+3721+\left (1146-162 i+\left (1098-915 i\right ) \ln \left (x \right )\right ) x^{i}}{22326 x} \]

✓ Mathematica. Time used: 0.482 (sec). Leaf size: 67

ode=x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+y[x]==(Log[x]*Sin[Log[x]]+1)/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {3721 \left (6 c_2 x^{3+\sqrt {3}}+6 c_1 x^{3-\sqrt {3}}+1\right )+6 (305 \log (x)+54) \sin (\log (x))+12 (183 \log (x)+191) \cos (\log (x))}{22326 x} \]

✓ Sympy. Time used: 0.832 (sec). Leaf size: 65

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 3*x*Derivative(y(x), x) + y(x) - (log(x)*sin(log(x)) + 1)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {22326 x \left (C_{1} x^{2 - \sqrt {3}} + C_{2} x^{\sqrt {3} + 2}\right ) + 1830 \log {\left (x \right )} \sin {\left (\log {\left (x \right )} \right )} + 2196 \log {\left (x \right )} \cos {\left (\log {\left (x \right )} \right )} + 324 \sin {\left (\log {\left (x \right )} \right )} + 2292 \cos {\left (\log {\left (x \right )} \right )} + 3721}{22326 x} \]