Internal problem ID [15422]
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 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 657.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=\frac {{\mathrm e}^{x}}{x^{2}+1}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/(x^2+1),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (c_{2} +c_{1} x -\frac {\ln \left (x^{2}+1\right )}{2}+x \arctan \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 35
DSolve[y''[x]-2*y'[x]+y[x]==Exp[x]/(1+x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^x \left (2 x \arctan (x)-\log \left (x^2+1\right )+2 (c_2 x+c_1)\right ) \]