73.14.16 problem 21.14 (b)

Internal problem ID [15426]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 21. Nonhomogeneous equations in general. Additional exercises page 391
Problem number : 21.14 (b)
Date solved : Tuesday, January 28, 2025 at 07:55:18 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-4 x y^{\prime }+6 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve(x^2*diff(y(x),x$2)-4*x*diff(y(x),x)+6*y(x)=x,y(x), singsol=all)
 

\[ y = c_{2} x^{3}+c_{1} x^{2}+\frac {1}{2} x \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 23

DSolve[x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+6*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 x^3+c_1 x^2+\frac {x}{2} \]