33.2.9 problem Problem 11.52

Internal problem ID [7813]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 11. THE METHOD OF UNDETERMINED COEFFICIENTS. Supplementary Problems. page 101
Problem number : Problem 11.52
Date solved : Tuesday, September 30, 2025 at 05:05:52 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}+1 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+3*diff(y(x),x)-y(x) = exp(x)+1; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.126 (sec). Leaf size: 101

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

\begin{align*} y(x)&\to e^x x \int _1^x\left (-1-e^{-K[2]}\right ) K[2]dK[2]+e^x \int _1^x\frac {1}{2} e^{-K[1]} \left (1+e^{K[1]}\right ) K[1]^2dK[1]+\frac {e^x x^3}{2}-\frac {x^2}{2}+c_3 e^x x^2+c_2 e^x x+c_1 e^x \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 19

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

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