8.11.38 problem 61

Internal problem ID [906]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 61
Date solved : Wednesday, February 05, 2025 at 04:44:05 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: 0.003 (sec). Leaf size: 17

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

\[ y = \sin \left (\ln \left (x \right )\right ) c_2 +\cos \left (\ln \left (x \right )\right ) c_1 +\ln \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 20

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

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