73.10.15 problem 15.6 (b)

Internal problem ID [15239]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 15. General solutions to Homogeneous linear differential equations. Additional exercises page 294
Problem number : 15.6 (b)
Date solved : Monday, March 31, 2025 at 01:32:06 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 )&=0\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 15

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

\[ y = \frac {{\mathrm e}^{x}}{4}-\frac {{\mathrm e}^{-3 x}}{4} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{4} e^{-3 x} \left (e^{4 x}-1\right ) \]

✓ Sympy. Time used: 0.187 (sec). Leaf size: 15

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): 0, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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