12.19.62 problem section 9.3, problem 62

Internal problem ID [2209]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 62
Date solved : Tuesday, March 04, 2025 at 01:51:46 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (-3 x^{2}-4 x +5\right ) \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 29

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)*(-3*x^2-4*x+5); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 37

ode=D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==Exp[2*x]*(5-4*x-3*x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (e^x \left (x^3+2 x^2+x+4+c_2\right )+c_3 e^{2 x}+c_1\right ) \]

✓ Sympy. Time used: 0.355 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((3*x**2 + 4*x - 5)*exp(2*x) - 6*y(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)
 

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