83.15.2 problem 2

Internal problem ID [19108]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (G) at page 45
Problem number : 2
Date solved : Thursday, March 13, 2025 at 01:41:51 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 21

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

\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+\left (c_3 x +c_{1} \right ) {\mathrm e}^{x}+x +1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 29

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

\[ y(x)\to x+c_3 e^x x+c_1 e^{-x}+c_2 e^x+1 \]

✓ Sympy. Time used: 0.196 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-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)
 

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