35.7.19 problem 22

Internal problem ID [6201]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 22
Date solved : Monday, January 27, 2025 at 01:47:36 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 19

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

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