23.5.70 problem 70

Internal problem ID [6679]
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 : 70
Date solved : Tuesday, September 30, 2025 at 03:50:47 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} 18 \,{\mathrm e}^{x}-3 y-11 y^{\prime }-8 y^{\prime \prime }+4 y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 23

ode:=18*exp(x)-3*y(x)-11*diff(y(x),x)-8*diff(diff(y(x),x),x)+4*diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 37

ode=18*E^x - 3*y[x] - 11*D[y[x],x] - 8*D[y[x],{x,2}] + 4*D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{-x/2} \left (e^{3 x/2}+c_2 x+c_3 e^{7 x/2}+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.122 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x) + 18*exp(x) - 11*Derivative(y(x), x) - 8*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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