73.15.76 problem 22.15 (c)

Internal problem ID [15507]
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 : Tuesday, January 28, 2025 at 08:00:24 AM
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*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

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

\[ y = \frac {2 c_{2} +\int \frac {c_{1} +17 \cos \left (2 \ln \left (x \right )\right ) x +34 x \sin \left (2 \ln \left (x \right )\right )}{x^{{3}/{2}}}d x}{2 \sqrt {x}} \]

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 53

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

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