28.2.69 problem 69

Internal problem ID [4512]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 69
Date solved : Monday, January 27, 2025 at 09:22:31 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 25

dsolve((x-2)^2*diff(y(x),x$2)-3*(x-2)*diff(y(x),x)+4*y(x)=x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 31

DSolve[(x-2)^2*D[y[x],{x,2}]-3*(x-2)*D[y[x],x]+4*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

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