Internal problem ID [5178]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {L y^{\prime }+R y-E \,{\mathrm e}^{i \omega x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.023 (sec). Leaf size: 38
dsolve([L*diff(y(x),x)+R*y(x)=E*exp(I*omega*x),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {E \left ({\mathrm e}^{\frac {x \left (i L \omega +R \right )}{L}}-1\right ) {\mathrm e}^{-\frac {R x}{L}}}{i L \omega +R} \]
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 43
DSolve[{L*y'[x]+R*y[x]==E0*Exp[I*\[Omega]*x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} 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 } \\ \end{align*}