15.14.25 problem 25

Internal problem ID [3197]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 25
Date solved : Tuesday, March 04, 2025 at 04:05:46 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 33

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

\[ y = \frac {\left (-x^{3}+3 c_2 -6 x \right ) {\mathrm e}^{2 x}}{3}+{\mathrm e}^{x} c_{1} +c_3 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 37

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

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

✓ Sympy. Time used: 0.351 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*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)
 

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