20.9.21 problem Problem 21

Internal problem ID [3765]
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
Date solved : Monday, January 27, 2025 at 08:01:04 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=\frac {2 \,{\mathrm e}^{-x}}{x^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 39

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)
 

\[ y \left (x \right ) = {\mathrm e}^{-x} \left (x^{2} \arctan \left (x \right )-x \ln \left (x^{2}+1\right )-\arctan \left (x \right )+x +c_{1} +c_{2} x +c_3 \,x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]+3*D[y[x],x]+y[x]==2*Exp[-x]/(1+x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (\left (x^2-1\right ) \arctan (x)-x \log \left (x^2+1\right )+c_3 x^2+x+c_2 x+c_1\right ) \]