75.15.21 problem 452

Internal problem ID [16901]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.2 Homogeneous differential equations with constant coefficients. Exercises page 121
Problem number : 452
Date solved : Monday, March 31, 2025 at 03:35:01 PM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

\[ y = c_1 +c_2 \,{\mathrm e}^{\frac {x}{2}}+c_3 \,{\mathrm e}^{x} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 25

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

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

✓ Sympy. Time used: 0.126 (sec). Leaf size: 15

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

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