77.16.1 problem 1

Internal problem ID [20475]
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 (H) at page 47
Problem number : 1
Date solved : Thursday, October 02, 2025 at 06:03:14 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 2 y-3 y^{\prime }+y^{\prime \prime \prime }&={\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(y(x),x)+2*y(x) = exp(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to e^x \left (\frac {x^2}{6}+\left (-\frac {1}{9}+c_3\right ) x+\frac {1}{27}+c_2\right )+c_1 e^{-2 x} \end{align*}

✓ Sympy. Time used: 0.151 (sec). Leaf size: 20

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

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