89.11.28 problem 28

Internal problem ID [24553]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 8. Linear Differential Equations with constant coefficients. Exercises at page 117
Problem number : 28
Date solved : Thursday, October 02, 2025 at 10:46:04 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+3 y^{\prime }-10 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y \left (2\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.055 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)+3*diff(y(x),x)-10*y(x) = 0; 
ic:=[y(0) = 0, y(2) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = {\mathrm e}^{3-\frac {3 x}{2}} \sinh \left (\frac {7 x}{2}\right ) \operatorname {csch}\left (7\right ) \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 27

ode=D[y[x],{x,2}] +3*D[y[x],x] -10*y[x]==0; 
ic={y[0]==0,y[2] ==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {e^{10-5 x} \left (e^{7 x}-1\right )}{e^{14}-1} \end{align*}

✓ Sympy. Time used: 0.095 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*y(x) - Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 3, Subs(Derivative(y(x), x), x, 0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

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