28.2.66 problem 66

Internal problem ID [4509]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 66
Date solved : Monday, January 27, 2025 at 09:22:10 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 19

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

\[ y(x)\to \log (x)+c_1 x+c_2 x \log (x)+2 \]