67.15.76 problem 22.15 (c)

Internal problem ID [16794]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 22. Method of undetermined coefficients. Additional exercises page 412
Problem number : 22.15 (c)
Date solved : Thursday, October 02, 2025 at 01:38:57 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=85 \cos \left (2 \ln \left (x \right )\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=2*x^2*diff(diff(y(x),x),x)+5*x*diff(y(x),x)+y(x) = 85*cos(2*ln(x)); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 c_2 +\int \frac {c_1 +17 \cos \left (2 \ln \left (x \right )\right ) x +34 x \sin \left (2 \ln \left (x \right )\right )}{x^{{3}/{2}}}d x}{2 \sqrt {x}} \]

✓ Mathematica. Time used: 0.159 (sec). Leaf size: 53

ode=2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+y[x]==85*Cos[2*Log[x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {\int _1^x-85 \cos (2 \log (K[1]))dK[1]+(5-20 i) x^{1+2 i}+(5+20 i) x^{1-2 i}+c_2 \sqrt {x}+c_1}{x} \end{align*}

✓ Sympy. Time used: 0.303 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) + 5*x*Derivative(y(x), x) + y(x) - 85*cos(2*log(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1}}{x} + \frac {C_{2}}{\sqrt {x}} + 6 \sin {\left (2 \log {\left (x \right )} \right )} - 7 \cos {\left (2 \log {\left (x \right )} \right )} \]