64.13.27 problem 27

Internal problem ID [13557]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.5. The Cauchy-Euler Equation. Exercises page 169
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 05:52:54 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-6 y&=\ln \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{6}}\\ y^{\prime }\left (1\right )&=-{\frac {1}{6}} \end{align*}

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 20

dsolve([x^2*diff(y(x),x$2)-6*y(x)=ln(x),y(1) = 1/6, D(y)(1) = -1/6],y(x), singsol=all)
 

\[ y = \frac {1}{12 x^{2}}+\frac {x^{3}}{18}-\frac {\ln \left (x \right )}{6}+\frac {1}{36} \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 29

DSolve[{x^2*D[y[x],{x,2}]-6*y[x]==Log[x],{y[1]==1/6,Derivative[1][y][1]==-1/6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 x^5+x^2-6 x^2 \log (x)+3}{36 x^2} \]