Internal problem ID [11881]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-6 y=\ln \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (1\right ) = {\frac {1}{6}}, y^{\prime }\left (1\right ) = -{\frac {1}{6}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \frac {1}{12 x^{2}}+\frac {x^{3}}{18}-\frac {\ln \left (x \right )}{6}+\frac {1}{36} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 29
DSolve[{x^2*y''[x]-6*y[x]==Log[x],{y[1]==1/6,y'[1]==-1/6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 x^5+x^2-6 x^2 \log (x)+3}{36 x^2} \]