Internal problem ID [11879]
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: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+2 y^{\prime } x -6 y=10 x^{2}} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = -6] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve([x^2*diff(y(x),x$2)+2*x*diff(y(x),x)-6*y(x)=10*x^2,y(1) = 1, D(y)(1) = -6],y(x), singsol=all)
\[ y \left (x \right ) = \frac {2 x^{5} \ln \left (x \right )-x^{5}+2}{x^{3}} \]
✓ Solution by Mathematica
Time used: 0.018 (sec). Leaf size: 23
DSolve[{x^2*y''[x]+2*x*y'[x]-6*y[x]==10*x^2,{y[1]==1,y'[1]==-6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-x^5+2 x^5 \log (x)+2}{x^3} \]