82.5.2 problem 29-3

Internal problem ID [21843]
Book : The Differential Equations Problem Solver. VOL. II. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 29. Second Order Boundary Value Problems. Page 959
Problem number : 29-3
Date solved : Thursday, October 02, 2025 at 08:02:46 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 36

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

\[ y = \frac {\left (2 \,{\mathrm e}^{3+4 x}+3 \,{\mathrm e}^{4 x}+{\mathrm e}^{4}-2 \,{\mathrm e}^{3}\right ) {\mathrm e}^{-3 x}}{{\mathrm e}^{4}+3} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to \frac {e^{-3 x} \left (3 e^{4 x}+2 e^{4 x+3}-2 e^3+e^4\right )}{3+e^4} \end{align*}

✓ Sympy. Time used: 0.110 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = \frac {\left (3 + 2 e^{3}\right ) e^{x}}{3 + e^{4}} + \frac {\left (- 2 e^{3} + e^{4}\right ) e^{- 3 x}}{3 + e^{4}} \]