Internal problem ID [2794]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of
Parameters Method. page 556
Problem number: Problem 21.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y=\frac {2 \,{\mathrm e}^{-x}}{x^{2}+1}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 64
dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=2*exp(-x)/(1+x^2),y(x), singsol=all)
\[ y \left (x \right ) = \arctan \left (x \right ) x^{2} {\mathrm e}^{-x}-\ln \left (x^{2}+1\right ) x \,{\mathrm e}^{-x}-{\mathrm e}^{-x} \arctan \left (x \right )+x \,{\mathrm e}^{-x}+{\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{-x} x +c_{3} x^{2} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 42
DSolve[y'''[x]+3*y''[x]+3*y'[x]+y[x]==2*Exp[-x]/(1+x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (\left (x^2-1\right ) \arctan (x)-x \log \left (x^2+1\right )+c_3 x^2+x+c_2 x+c_1\right ) \]