77.1.128 problem 155 (page 236)

Internal problem ID [18018]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 155 (page 236)
Date solved : Tuesday, January 28, 2025 at 11:20:02 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 28

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

\[ y = \frac {\left (2 x -3\right ) {\mathrm e}^{x}}{8}+\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} +c_{3} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 36

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

\[ y(x)\to \frac {1}{8} e^x (2 x-3)+c_3 e^{-x}+c_1 \cos (x)+c_2 \sin (x) \]