49.2.9 problem 5

Internal problem ID [7599]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.6 Introduction– Linear equations of First Order. Page 41
Problem number : 5
Date solved : Monday, January 27, 2025 at 03:07:05 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} L y^{\prime }+R y&=E \,{\mathrm e}^{i \omega x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 36

dsolve([L*diff(y(x),x)+R*y(x)=E*exp(I*omega*x),y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {E \left ({\mathrm e}^{\frac {x \left (i L \omega +R \right )}{L}}-1\right ) {\mathrm e}^{-\frac {R x}{L}}}{i L \omega +R} \]

✓ Solution by Mathematica

Time used: 0.113 (sec). Leaf size: 43

DSolve[{L*D[y[x],x]+R*y[x]==E0*Exp[I*\[Omega]*x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\text {E0} e^{-\frac {R x}{L}} \left (-1+e^{\frac {x (R+i L \omega )}{L}}\right )}{R+i L \omega } \]