73.15.79 problem 22.15 (f)

Internal problem ID [15510]
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 (f)
Date solved : Tuesday, January 28, 2025 at 08:00:33 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} 2 x^{2} y^{\prime \prime }+5 x y^{\prime }+y&=\frac {10}{x} \end{align*}

✓ Solution by Maple

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

dsolve(2*x^2*diff(y(x),x$2)+5*x*diff(y(x),x)+y(x)=10/x,y(x), singsol=all)
 

\[ y = \frac {-10 \sqrt {x}\, \ln \left (x \right )+c_{2} x +\left (c_{1} -20\right ) \sqrt {x}}{x^{{3}/{2}}} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 25

DSolve[2*x^2*D[y[x],{x,2}]+5*x*D[y[x],x]+y[x]==10/x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-10 \log (x)+c_2 \sqrt {x}-20+c_1}{x} \]