23.5.150 problem 150

Internal problem ID [6759]
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 : 150
Date solved : Tuesday, September 30, 2025 at 03:51:27 PM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} -2 y+5 y^{\prime }-3 y^{\prime \prime }-y^{\prime \prime \prime }+y^{\prime \prime \prime \prime }&={\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 30

ode:=-2*y(x)+5*diff(y(x),x)-3*diff(diff(y(x),x),x)-diff(diff(diff(y(x),x),x),x)+diff(diff(diff(diff(y(x),x),x),x),x) = exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 \,{\mathrm e}^{-2 x}+\frac {{\mathrm e}^{3 x}}{40}+\left (c_4 \,x^{2}+c_3 x +c_1 \right ) {\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.043 (sec). Leaf size: 39

ode=-2*y[x] + 5*D[y[x],x] - 3*D[y[x],{x,2}] - D[y[x],{x,3}] + D[y[x],{x,4}] == E^(3*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{3 x}}{40}+c_1 e^{-2 x}+e^x (x (c_4 x+c_3)+c_2) \end{align*}

✓ Sympy. Time used: 0.177 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-2*y(x) - exp(3*x) + 5*Derivative(y(x), x) - 3*Derivative(y(x), (x, 2)) - Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{4} e^{- 2 x} + \left (C_{1} + x \left (C_{2} + C_{3} x\right )\right ) e^{x} + \frac {e^{3 x}}{40} \]