58.11.12 problem 12

Internal problem ID [14743]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page 151
Problem number : 12
Date solved : Thursday, October 02, 2025 at 09:50:42 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime \prime }-4 y^{\prime \prime }-5 y^{\prime }+3 y&=3 x^{3}-8 x \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 35

ode:=4*diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)-5*diff(y(x),x)+3*y(x) = 3*x^3-8*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{3}+5 x^{2}+22 x +42+c_1 \,{\mathrm e}^{-x}+c_2 \,{\mathrm e}^{\frac {x}{2}}+c_3 \,{\mathrm e}^{\frac {3 x}{2}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 46

ode=4*D[y[x],{x,3}]-4*D[y[x],{x,2}]-5*D[y[x],x]+3*y[x]==3*x^3-8*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^3+5 x^2+22 x+c_1 e^{x/2}+c_2 e^{3 x/2}+c_3 e^{-x}+42 \end{align*}

✓ Sympy. Time used: 0.139 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**3 + 8*x + 3*y(x) - 5*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{\frac {x}{2}} + C_{3} e^{\frac {3 x}{2}} + x^{3} + 5 x^{2} + 22 x + 42 \]