71.10.14 problem 19

Internal problem ID [14438]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number : 19
Date solved : Monday, March 31, 2025 at 12:27:10 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }-i y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.025 (sec). Leaf size: 8

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

\[ y = {\mathrm e}^{i x} \]

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 12

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

\[ y(x)\to e^{i x} \]

✓ Sympy. Time used: 0.111 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = e^{- x \operatorname {complex}{\left (0,-1 \right )}} \]