83.15.1 problem 1

Internal problem ID [19107]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (G) at page 45
Problem number : 1
Date solved : Thursday, March 13, 2025 at 01:41:50 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-4 y^{\prime \prime }+5 y^{\prime }-2&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 34

ode:=diff(diff(diff(y(x),x),x),x)-4*diff(diff(y(x),x),x)+5*diff(y(x),x)-2 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (\left (2 c_{1} -c_{2} \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_{1} +2 c_{2} \right )\right ) {\mathrm e}^{2 x}}{5}+\frac {2 x}{5}+c_3 \]

✓ Mathematica. Time used: 0.142 (sec). Leaf size: 47

ode=D[y[x],{x,3}]-4*D[y[x],{x,2}]+5*D[y[x],x]-2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{5} \left (2 x-(c_1-2 c_2) e^{2 x} \cos (x)+(2 c_1+c_2) e^{2 x} \sin (x)\right )+c_3 \]

✓ Sympy. Time used: 0.171 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*Derivative(y(x), x) - 4*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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