77.1.128 problem 155 (page 236)

Internal problem ID [17939]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 155 (page 236)
Date solved : Thursday, March 13, 2025 at 11:11:03 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*}

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

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)+diff(y(x),x)+y(x) = x*exp(x); 
dsolve(ode,y(x), singsol=all);
 

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

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

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

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

✓ Sympy. Time used: 0.187 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*exp(x) + y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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