82.33.21 problem Ex. 21

Internal problem ID [18914]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VI. Linear equations with constant coefficients. Examples on chapter VI, page 80
Problem number : Ex. 21
Date solved : Tuesday, January 28, 2025 at 12:36:21 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

dsolve(diff(y(x),x$3)+3*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=exp(-x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{-x} \left (\frac {1}{6} x^{3}+c_{1} +c_{2} x +c_3 \,x^{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 34

DSolve[D[y[x],{x,3}]+3*D[y[x],{x,2}]+3*D[y[x],x]+y[x]==Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{-x} \left (x^3+6 c_3 x^2+6 c_2 x+6 c_1\right ) \]