18.2.10 problem Problem 15.21

Internal problem ID [3493]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page 523
Problem number : Problem 15.21
Date solved : Monday, January 27, 2025 at 07:39:39 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 25

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

\[ y(x)\to \frac {1}{2} x \left (\log ^2(x)+2 c_2 \log (x)+2 c_1\right ) \]