88.10.9 problem 9

Internal problem ID [24044]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 52
Problem number : 9
Date solved : Thursday, October 02, 2025 at 09:55:09 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime }+11 y^{\prime }+4 y&=2 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 18

ode:=6*diff(diff(y(x),x),x)+11*diff(y(x),x)+4*y(x) = 2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-\frac {x}{2}} c_2 +{\mathrm e}^{-\frac {4 x}{3}} c_1 +\frac {1}{2} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 29

ode=6*D[y[x],{x,2}]+11*D[y[x],x]+4*y[x]==2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^{-4 x/3}+c_2 e^{-x/2}+\frac {1}{2} \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) + 11*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)) - 2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- \frac {4 x}{3}} + C_{2} e^{- \frac {x}{2}} + \frac {1}{2} \]