29.8.27 problem 27

Internal problem ID [7369]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 27
Date solved : Tuesday, September 30, 2025 at 04:29:56 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=4 \\ \end{align*}

✓ Maple. Time used: 0.043 (sec). Leaf size: 12

ode:=diff(diff(y(x),x),x)+diff(y(x),x)-6*y(x) = 6; 
ic:=[y(0) = 1, D(y)(0) = 4]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 \,{\mathrm e}^{2 x}-1 \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 14

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

\begin{align*} y(x)&\to 2 e^{2 x}-1 \end{align*}

✓ Sympy. Time used: 0.099 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) + Derivative(y(x), x) + Derivative(y(x), (x, 2)) - 6,0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 4} 
dsolve(ode,func=y(x),ics=ics)
 

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