Internal problem ID [15397]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.4 Nonhomogeneous linear equations with
constant coefficients. The Euler equations. Exercises page 143
Problem number: 628.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }+y=x \left (6-\ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)+y(x)=x*(6-ln(x)),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\ln \left (x \right )\right ) c_{2} +\cos \left (\ln \left (x \right )\right ) c_{1} -\frac {x \left (\ln \left (x \right )-7\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.138 (sec). Leaf size: 27
DSolve[x^2*y''[x]+x*y'[x]+y[x]==x*(6-Log[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{2} x (\log (x)-7)+c_1 \cos (\log (x))+c_2 \sin (\log (x)) \]