28.2.20 problem 20

Internal problem ID [4463]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 20
Date solved : Sunday, March 30, 2025 at 03:23:16 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime }&=x^{2}+x \,{\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 41

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+3*diff(y(x),x) = x^2+x*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (1-2 x \right ) {\mathrm e}^{2 x}}{4}+\frac {x^{3}}{9}+\frac {4 x^{2}}{9}+{\mathrm e}^{x} c_1 +\frac {{\mathrm e}^{3 x} c_2}{3}+\frac {26 x}{27}+c_3 \]

✓ Mathematica. Time used: 0.385 (sec). Leaf size: 58

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]+3*D[y[x],x]==x^2+x*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {x^3}{9}+\frac {4 x^2}{9}+\frac {26 x}{27}+\frac {1}{4} e^{2 x} (1-2 x)+c_1 e^x+\frac {1}{3} c_2 e^{3 x}+c_3 \]

✓ Sympy. Time used: 0.269 (sec). Leaf size: 44

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - x*exp(2*x) + 3*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{x} + C_{3} e^{3 x} + \frac {x^{3}}{9} + \frac {4 x^{2}}{9} + \frac {26 x}{27} + \frac {\left (1 - 2 x\right ) e^{2 x}}{4} \]