12.2.8 problem Problem 15.9(a)

Internal problem ID [3491]
Book : Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition, 2002
Section : Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page 523
Problem number : Problem 15.9(a)
Date solved : Tuesday, September 30, 2025 at 06:40:44 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-12 y^{\prime }+16 y&=32 x -8 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 25

ode:=diff(diff(diff(y(x),x),x),x)-12*diff(y(x),x)+16*y(x) = 32*x-8; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_3 x +c_2 \right ) {\mathrm e}^{2 x}+c_1 \,{\mathrm e}^{-4 x}+2 x +1 \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 35

ode=D[y[x],{x,3}]-12*D[y[x],x]+16*y[x]==32*x-8; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-4 x}+c_2 e^{2 x}+x \left (2+c_3 e^{2 x}\right )+1 \end{align*}

✓ Sympy. Time used: 0.148 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-32*x + 16*y(x) - 12*Derivative(y(x), x) + Derivative(y(x), (x, 3)) + 8,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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