23.5.60 problem 60

Internal problem ID [6669]
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 : 60
Date solved : Tuesday, September 30, 2025 at 03:50:40 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} \operatorname {a3} y+\operatorname {a2} y^{\prime }+\operatorname {a1} y^{\prime \prime }+y^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 490

ode:=a3*y(x)+a2*diff(y(x),x)+a1*diff(diff(y(x),x),x)+diff(diff(diff(y(x),x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 84

ode=a3*y[x] + a2*D[y[x],x] + a1*D[y[x],{x,2}] + D[y[x],{x,3}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a1}+\text {$\#$1} \text {a2}+\text {a3}\&,1\right ]}+c_2 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a1}+\text {$\#$1} \text {a2}+\text {a3}\&,2\right ]}+c_3 e^{x \text {Root}\left [\text {$\#$1}^3+\text {$\#$1}^2 \text {a1}+\text {$\#$1} \text {a2}+\text {a3}\&,3\right ]} \end{align*}

✓ Sympy. Time used: 0.889 (sec). Leaf size: 653

from sympy import * 
x = symbols("x") 
a1 = symbols("a1") 
a2 = symbols("a2") 
a3 = symbols("a3") 
y = Function("y") 
ode = Eq(a1*Derivative(y(x), (x, 2)) + a2*Derivative(y(x), x) + a3*y(x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]