Internal problem ID [11870]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+4 y^{\prime } x +2 y=4 \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(x^2*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=4*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = 2 \ln \left (x \right )+\frac {c_{1}}{x}-3+\frac {c_{2}}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 23
DSolve[x^2*y''[x]+4*x*y'[x]+2*y[x]==4*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1}{x^2}+2 \log (x)+\frac {c_2}{x}-3 \]