76.13.32 problem 32

Internal problem ID [17543]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.3 (Linear homogeneous equations with constant coefficients). Problems at page 239
Problem number : 32
Date solved : Monday, March 31, 2025 at 04:16:57 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 6 y^{\prime \prime }-5 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Maple. Time used: 0.047 (sec). Leaf size: 17

ode:=6*diff(diff(y(x),x),x)-5*diff(y(x),x)+y(x) = 0; 
ic:=y(0) = 4, D(y)(0) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -8 \,{\mathrm e}^{\frac {x}{2}}+12 \,{\mathrm e}^{\frac {x}{3}} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

ode=6*D[y[x],{x,2}]-5*D[y[x],x]+y[x]==0; 
ic={y[0]==4,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 12 e^{x/3}-8 e^{x/2} \]

✓ Sympy. Time used: 0.175 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 5*Derivative(y(x), x) + 6*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 4, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 12 e^{\frac {x}{3}} - 8 e^{\frac {x}{2}} \]