15.14.23 problem 23

Internal problem ID [3195]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 23, page 106
Problem number : 23
Date solved : Sunday, March 30, 2025 at 01:20:57 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x) = exp(2*x)*(x-3); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-2 x +7\right ) {\mathrm e}^{2 x}}{16}+c_2 x +\frac {{\mathrm e}^{4 x} c_1}{16}+c_3 \]

✓ Mathematica. Time used: 0.233 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{16} e^{2 x} \left (-2 x+c_1 e^{2 x}+7\right )+c_3 x+c_2 \]

✓ Sympy. Time used: 0.120 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = C_{1} + C_{3} e^{4 x} + x \left (C_{2} - \frac {e^{2 x}}{8}\right ) + \frac {7 e^{2 x}}{16} \]