60.2.3 problem Problem 3

Internal problem ID [15183]
Book : Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS, MOSCOW, Third printing 1977.
Section : Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER. Problems page 172
Problem number : Problem 3
Date solved : Thursday, October 02, 2025 at 10:06:57 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime }+y^{\prime \prime \prime }-3 y^{\prime \prime }&=0 \end{align*}

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

ode:=diff(y(x),x)+diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 +c_2 \,{\mathrm e}^{\frac {\left (3+\sqrt {5}\right ) x}{2}}+c_3 \,{\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) x}{2}} \]

✓ Mathematica. Time used: 0.117 (sec). Leaf size: 57

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

\begin{align*} y(x)&\to \frac {1}{2} e^{-\frac {1}{2} \left (\sqrt {5}-3\right ) x} \left (\left (3+\sqrt {5}\right ) c_1-\left (\sqrt {5}-3\right ) c_2 e^{\sqrt {5} x}\right )+c_3 \end{align*}

✓ Sympy. Time used: 0.083 (sec). Leaf size: 31

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

\[ y{\left (x \right )} = C_{1} + C_{2} e^{\frac {x \left (3 - \sqrt {5}\right )}{2}} + C_{3} e^{\frac {x \left (\sqrt {5} + 3\right )}{2}} \]