64.13.14 problem 14

Internal problem ID [13544]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 05:52:22 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 22

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

\[ y(x)\to c_2 x^3+c_1 x^2+2 x-1 \]