Internal problem ID [15398]
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: 629.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-2 y=\sin \left (\ln \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(x^2*diff(y(x),x$2)-2*y(x)=sin(ln(x)),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}+c_{2} x^{2}+\frac {\cos \left (\ln \left (x \right )\right )}{10}-\frac {3 \sin \left (\ln \left (x \right )\right )}{10} \]
✓ Solution by Mathematica
Time used: 0.044 (sec). Leaf size: 31
DSolve[x^2*y''[x]-2*y[x]==Sin[Log[x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^2+\frac {c_1}{x}+\frac {1}{10} (\cos (\log (x))-3 \sin (\log (x))) \]