4.7.23 problem 25

Internal problem ID [1271]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 25
Date solved : Tuesday, September 30, 2025 at 04:31:58 AM
CAS classification : [[_2nd_order, _missing_x]]

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

With initial conditions

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

✓ Maple. Time used: 0.059 (sec). Leaf size: 27

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

\[ y = \frac {\left (4-2 \beta \right ) {\mathrm e}^{\frac {x}{2}}}{5}+\frac {\left (2 \beta +1\right ) {\mathrm e}^{-2 x}}{5} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 67

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

\begin{align*} y(x)&\to \frac {1}{34} e^{-\frac {1}{2} \left (3+\sqrt {17}\right ) x} \left (2 \sqrt {17} \beta +\left (-2 \sqrt {17} \beta +3 \sqrt {17}+17\right ) e^{\sqrt {17} x}-3 \sqrt {17}+17\right ) \end{align*}

✗ Sympy

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

Timed Out