54.4.13 problem 1466

Internal problem ID [12735]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1466
Date solved : Wednesday, October 01, 2025 at 02:21:29 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 a y^{\prime \prime }+3 a^{2} y^{\prime }-a^{3} y-{\mathrm e}^{a x}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

ode:=diff(diff(diff(y(x),x),x),x)-3*a*diff(diff(y(x),x),x)+3*a^2*diff(y(x),x)-a^3*y(x)-exp(a*x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{a x} \left (\frac {1}{6} x^{3}+c_1 +c_2 x +c_3 \,x^{2}\right ) \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 34

ode=-E^(a*x) - a^3*y[x] + 3*a^2*D[y[x],x] - 3*a*D[y[x],{x,2}] + Derivative[3][y][x] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.186 (sec). Leaf size: 19

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

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