83.49.25 problem Ex 25 page 140

Internal problem ID [19567]
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 VIII. Linear equations of second order
Problem number : Ex 25 page 140
Date solved : Monday, March 31, 2025 at 07:33:44 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-6*diff(diff(y(x),x),x)+11*diff(y(x),x)-6*y(x) = exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 30

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (e^x (-x+c_2)+c_3 e^{2 x}+c_1\right ) \]

✓ Sympy. Time used: 0.234 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - exp(2*x) + 11*Derivative(y(x), x) - 6*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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