77.1.129 problem 156 (page 236)

Internal problem ID [17948]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 156 (page 236)
Date solved : Monday, March 31, 2025 at 04:52:10 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+6 y^{\prime \prime }-4 y^{\prime }+y&=\left (x +1\right ) {\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 39

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-4*diff(diff(diff(y(x),x),x),x)+6*diff(diff(y(x),x),x)-4*diff(y(x),x)+y(x) = (1+x)*exp(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{x} \left (x^{5}+5 x^{4}+\left (120 c_4 +4\right ) x^{3}+120 c_3 \,x^{2}+120 c_2 x +120 c_1 \right )}{120} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 42

ode=D[y[x],{x,4}]-4*D[y[x],{x,3}]+6*D[y[x],{x,2}]-4*D[y[x],x]+y[x]==(x+1)*Exp[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (\frac {x^5}{120}+\frac {x^4}{24}+c_4 x^3+c_3 x^2+c_2 x+c_1\right ) \]

✓ Sympy. Time used: 0.372 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x + 1)*exp(x) + y(x) - 4*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) - 4*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + x \left (C_{3} + x \left (C_{4} + \frac {x^{2}}{120} + \frac {x}{24}\right )\right )\right )\right ) e^{x} \]