82.33.23 problem Ex. 23

Internal problem ID [18916]
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. 23
Date solved : Tuesday, January 28, 2025 at 12:36:22 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 33

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

\[ y \left (x \right ) = \frac {\left (x^{4}+4 x^{3}+\left (24 c_3 +3\right ) x^{2}+24 c_{2} x +24 c_{1} \right ) {\mathrm e}^{x}}{24} \]

✓ Solution by Mathematica

Time used: 0.008 (sec). Leaf size: 37

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

\[ y(x)\to \frac {1}{24} e^x \left (x^4+4 x^3+24 c_3 x^2+24 c_2 x+24 c_1\right ) \]