73.17.43 problem 43

Internal problem ID [15577]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 25. Review exercises for part III. page 447
Problem number : 43
Date solved : Tuesday, January 28, 2025 at 08:02:35 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+2 y&=6 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+2*y(x)=6,y(x), singsol=all)
 

\[ y = \frac {c_{2} \sin \left (\ln \left (x \right )\right )+c_{1} \cos \left (\ln \left (x \right )\right )+3 x}{x} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 25

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+2*y[x]==6,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {3 x+c_2 \cos (\log (x))+c_1 \sin (\log (x))}{x} \]