86.5.14 problem 14

Internal problem ID [23128]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 5. Linear equations of the second order with constant coefficients. Exercise 5a at page 74
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:23:09 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} 2 y^{\prime \prime }-15 y^{\prime }+27 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=7 \\ y^{\prime }\left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.018 (sec). Leaf size: 17

ode:=2*diff(diff(y(x),x),x)-15*diff(y(x),x)+27*y(x) = 0; 
ic:=[y(0) = 7, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {40 \,{\mathrm e}^{\frac {9 x}{2}}}{3}+\frac {61 \,{\mathrm e}^{3 x}}{3} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 25

ode=2*D[y[x],{x,2}]-15*D[y[x],x]+27*y[x]==0; 
ic={y[0]==7,Derivative[1][y][0] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{3} e^{3 x} \left (61-40 e^{3 x/2}\right ) \end{align*}

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

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(27*y(x) - 15*Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)),0) 
ics = {y(0): 7, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {40 e^{\frac {9 x}{2}}}{3} + \frac {61 e^{3 x}}{3} \]