71.10.14 problem 19

Internal problem ID [14509]
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 : Tuesday, January 28, 2025 at 06:42:48 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

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

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

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