77.44.4 problem Ex 4 page 36

Internal problem ID [20816]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter III. Ordinary linear differential equations with constant coefficients
Problem number : Ex 4 page 36
Date solved : Thursday, October 02, 2025 at 06:30:48 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 22

ode:=diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)+diff(y(x),x) = exp(-x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_3 -\frac {{\mathrm e}^{-x}}{4}+\left (c_2 +c_1 \left (x -1\right )\right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.084 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to -\frac {e^{-x}}{4}+e^x (c_2 (x-1)+c_1)+c_3 \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 19

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

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