83.11.4 problem 4

Internal problem ID [21993]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter VI. Linear equations with constant coefficients. Ex. XIII at page 106
Problem number : 4
Date solved : Thursday, October 02, 2025 at 08:21:30 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 3 y^{\prime \prime }-4 y^{\prime }+2 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 28

ode:=3*diff(diff(y(x),x),x)-4*diff(y(x),x)+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 42

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

\begin{align*} y(x)&\to e^{2 x/3} \left (c_2 \cos \left (\frac {\sqrt {2} x}{3}\right )+c_1 \sin \left (\frac {\sqrt {2} x}{3}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 32

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

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