6.19.24 problem section 9.3, problem 24

Internal problem ID [2171]
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 24
Date solved : Tuesday, September 30, 2025 at 05:24:34 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-3 y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{2 x} \left (12 x^{2}+26 x +15\right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 49

ode:=diff(diff(diff(diff(y(x),x),x),x),x)-3*diff(diff(diff(y(x),x),x),x)+4*diff(y(x),x) = exp(2*x)*(12*x^2+26*x+15); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (2 x^{4}+2 x^{3}+6 x^{2}+\left (6 c_3 -6\right ) x +6 c_2 -3 c_3 +3\right ) {\mathrm e}^{2 x}}{12}-c_1 \,{\mathrm e}^{-x}+c_4 \]

✓ Mathematica. Time used: 0.12 (sec). Leaf size: 58

ode=1*D[y[x],{x,4}]-3*D[y[x],{x,3}]-0*D[y[x],{x,2}]+4*D[y[x],x]+0*y[x]==Exp[2*x]*(15+26*x+12*x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{12} e^{2 x} \left (2 x^4+2 x^3+6 x^2+6 (-2+c_3) x+8+6 c_2-3 c_3\right )+c_1 \left (-e^{-x}\right )+c_4 \end{align*}

✓ Sympy. Time used: 0.297 (sec). Leaf size: 32

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-12*x**2 - 26*x - 15)*exp(2*x) + 4*Derivative(y(x), x) - 3*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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