Internal problem ID [10847]
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]]
\[ \boxed {\left (x +1\right )^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }+y-2 \cos \left (\ln \left (x +1\right )\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 29
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)
\[ y \left (x \right ) = c_{2} \sin \left (\ln \left (x +1\right )\right )+c_{1} \cos \left (\ln \left (x +1\right )\right )+\ln \left (x +1\right ) \sin \left (\ln \left (x +1\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.059 (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]
\begin{align*} y(x)\to \left (\frac {1}{2}+c_1\right ) \cos (\log (x+1))+(\log (x+1)+c_2) \sin (\log (x+1)) \\ \end{align*}