83.44.6 problem Ex 6 page 38

Internal problem ID [19463]
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 6 page 38
Date solved : Monday, March 31, 2025 at 07:19:27 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y&=\left (1+{\mathrm e}^{x}\right )^{2} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 44

ode:=diff(diff(diff(y(x),x),x),x)+y(x) = (exp(x)+1)^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 1+\frac {{\mathrm e}^{2 x}}{9}+{\mathrm e}^{\frac {x}{2}} \left (\cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_2 +\sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_3 \right )+{\mathrm e}^{x}+c_1 \,{\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.541 (sec). Leaf size: 78

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

\[ y(x)\to \frac {e^{-x}}{9}+e^x+\frac {e^{2 x}}{9}+c_1 e^{-x}+c_3 e^{x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_2 e^{x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+1 \]

✓ Sympy. Time used: 0.177 (sec). Leaf size: 48

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

\[ y{\left (x \right )} = C_{3} e^{- x} + \left (C_{1} \sin {\left (\frac {\sqrt {3} x}{2} \right )} + C_{2} \cos {\left (\frac {\sqrt {3} x}{2} \right )}\right ) e^{\frac {x}{2}} + \frac {e^{2 x}}{9} + e^{x} + 1 \]