62.22.1 problem Ex 1

Internal problem ID [12852]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 44. Roots of auxiliary equation repeated. Page 94
Problem number : Ex 1
Date solved : Monday, March 31, 2025 at 07:22:48 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 29

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

\[ y(x)\to e^{-x} \left (e^{3 x/2} (c_2 x+c_1)+c_3\right ) \]

✓ Sympy. Time used: 0.194 (sec). Leaf size: 17

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

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