87.12.21 problem 22

Internal problem ID [23469]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 93
Problem number : 22
Date solved : Thursday, October 02, 2025 at 09:42:07 PM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.028 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.118 (sec). Leaf size: 26

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

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