Internal problem ID [11871]
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: 17.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } x +4 y=2 x \ln \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+4*y(x)=2*x*ln(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (2 \ln \left (x \right )\right ) c_{2} +\cos \left (2 \ln \left (x \right )\right ) c_{1} +\frac {2 \ln \left (x \right ) x}{5}-\frac {4 x}{25} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 33
DSolve[x^2*y''[x]+x*y'[x]+4*y[x]==2*x*Log[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2}{25} x (5 \log (x)-2)+c_1 \cos (2 \log (x))+c_2 \sin (2 \log (x)) \]