1.11.11 problem 11

Internal problem ID [332]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 03:57:28 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=3 x -1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

ode:=diff(diff(diff(y(x),x),x),x)+4*diff(y(x),x) = 3*x-1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3 x^{2}}{8}+\frac {\sin \left (2 x \right ) c_1}{2}-\frac {\cos \left (2 x \right ) c_2}{2}-\frac {x}{4}+c_3 \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 38

ode=D[y[x],{x,3}]+4*D[y[x],x]==3*x-1; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{8} \left (3 x^2-2 x-4 c_2 \cos (2 x)+4 c_1 \sin (2 x)+8 c_3\right ) \end{align*}

✓ Sympy. Time used: 0.100 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x + 4*Derivative(y(x), x) + Derivative(y(x), (x, 3)) + 1,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} \sin {\left (2 x \right )} + C_{3} \cos {\left (2 x \right )} + \frac {3 x^{2}}{8} - \frac {x}{4} \]