23.5.34 problem 34

Internal problem ID [6643]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 34
Date solved : Tuesday, September 30, 2025 at 03:50:28 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 33

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

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

✓ Sympy. Time used: 0.097 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-exp(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)
 

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