4.7.11 problem 11

Internal problem ID [1259]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 11
Date solved : Tuesday, September 30, 2025 at 04:31:47 AM
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: 0.044 (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,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 48

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

\begin{align*} y(x)&\to \frac {4}{23} e^{5 x/12} \left (23 \cos \left (\frac {\sqrt {23} x}{12}\right )-5 \sqrt {23} \sin \left (\frac {\sqrt {23} x}{12}\right )\right ) \end{align*}

✓ Sympy. Time used: 0.100 (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)
 

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