Internal problem ID [12195]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\left (1+x \right )^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }+y=2 \cos \left (\ln \left (1+x \right )\right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve((1+x)^2*diff(y(x),x$2)+(1+x)*diff(y(x),x)+y(x)=2*cos(ln(1+x)),y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{2} +\ln \left (1+x \right )\right ) \sin \left (\ln \left (1+x \right )\right )+\cos \left (\ln \left (1+x \right )\right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 31
DSolve[(1+x)^2*y''[x]+(1+x)*y'[x]+y[x]==2*Cos[Log[1+x]],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (\frac {1}{2}+c_1\right ) \cos (\log (x+1))+(\log (x+1)+c_2) \sin (\log (x+1)) \]