12.19.26 problem section 9.3, problem 26

Internal problem ID [2173]
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 26
Date solved : Tuesday, March 04, 2025 at 01:51:07 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime \prime \prime }-5 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }-y&={\mathrm e}^{x} \left (11+12 x \right ) \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 35

ode:=2*diff(diff(diff(diff(y(x),x),x),x),x)-5*diff(diff(diff(y(x),x),x),x)+3*diff(diff(y(x),x),x)+diff(y(x),x)-y(x) = exp(x)*(11+12*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_4 \,{\mathrm e}^{-\frac {x}{2}}+\frac {{\mathrm e}^{x} \left (x^{4}+6 c_3 \,x^{2}+x^{3}+6 c_2 x +6 c_1 \right )}{6} \]

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 58

ode=2*D[y[x],{x,4}]-5*D[y[x],{x,3}]+3*D[y[x],{x,2}]+1*D[y[x],x]-1*y[x]==Exp[x]*(11+12*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^x \left (\frac {x^4}{6}+\frac {x^3}{6}+\left (-\frac {1}{3}+c_4\right ) x^2+\left (\frac {4}{9}+c_3\right ) x-\frac {8}{27}+c_2\right )+c_1 e^{-x/2} \]

✓ Sympy. Time used: 0.390 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-12*x - 11)*exp(x) - y(x) + Derivative(y(x), x) + 3*Derivative(y(x), (x, 2)) - 5*Derivative(y(x), (x, 3)) + 2*Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{4} e^{- \frac {x}{2}} + \left (C_{1} + x \left (C_{2} + x \left (C_{3} + \frac {x^{2}}{6} + \frac {x}{6}\right )\right )\right ) e^{x} \]