87.11.10 problem 10

Internal problem ID [23428]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 84
Problem number : 10
Date solved : Thursday, October 02, 2025 at 09:41:38 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+3 y&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 33

ode:=2*diff(diff(diff(y(x),x),x),x)-2*diff(diff(y(x),x),x)-diff(y(x),x)+3*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 42

ode=2*D[y[x],{x,3}]-2*D[y[x],{x,2}]-D[y[x],{x,1}]+3*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.164 (sec). Leaf size: 34

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

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