15.12.13 problem 13

Internal problem ID [3157]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 13
Date solved : Sunday, March 30, 2025 at 01:19:55 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

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

✓ Mathematica. Time used: 0.064 (sec). Leaf size: 30

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

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

✓ Sympy. Time used: 0.236 (sec). Leaf size: 19

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

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