Internal problem ID [5177]
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: 4.
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 \sin \left (\omega x \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 47
dsolve([L*diff(y(x),x)+R*y(x)=E*sin(omega*x),y(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = -\frac {E \left (L \cos \left (\omega x \right ) \omega -{\mathrm e}^{-\frac {R x}{L}} L \omega -\sin \left (\omega x \right ) R \right )}{\omega ^{2} L^{2}+R^{2}} \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 47
DSolve[{L*y'[x]+R*y[x]==E0*Sin[\[Omega]*x],{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\text {E0} \left (L \omega e^{-\frac {R x}{L}}-L \omega \cos (x \omega )+R \sin (x \omega )\right )}{L^2 \omega ^2+R^2} \\ \end{align*}