Internal problem ID [10217]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1894.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime \prime }\left (t \right )+a \left (x^{\prime }\left (t \right )-y^{\prime }\left (t \right )\right )+b_{1} x \left (t \right )&=c_{1} {\mathrm e}^{i \omega t}\\ y^{\prime \prime }\left (t \right )+a \left (y^{\prime }\left (t \right )-x^{\prime }\left (t \right )\right )+b_{2} y \left (t \right )&=c_{2} {\mathrm e}^{i \omega t} \end {align*}
✓ Solution by Maple
Time used: 2.032 (sec). Leaf size: 2571
dsolve([diff(x(t),t,t)+a*(diff(x(t),t)-diff(y(t),t))+b__1*x(t)=c__1*exp(I*omega*t),diff(y(t),t,t)+a*(diff(y(t),t)-diff(x(t),t))+b__2*y(t)=c__2*exp(I*omega*t)],singsol=all)
\begin{align*} \text {Expression too large to display} \\ y \left (t \right ) &= \frac {i {\mathrm e}^{i \omega t} c_{1} a \omega +i {\mathrm e}^{i \omega t} c_{2} a \omega -{\mathrm e}^{i \omega t} \omega ^{2} c_{2} +{\mathrm e}^{i \omega t} b_{1} c_{2}}{-2 i a \,\omega ^{3}+i a b_{1} \omega +i a b_{2} \omega +\omega ^{4}-b_{1} \omega ^{2}-b_{2} \omega ^{2}+b_{1} b_{2}}+c_{3} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (b_{1} +b_{2} \right ) \textit {\_Z}^{2}+\left (b_{1} a +b_{2} a \right ) \textit {\_Z} +b_{1} b_{2} , \operatorname {index} &=1\right ) t}+c_{4} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (b_{1} +b_{2} \right ) \textit {\_Z}^{2}+\left (b_{1} a +b_{2} a \right ) \textit {\_Z} +b_{1} b_{2} , \operatorname {index} &=2\right ) t}+c_{5} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (b_{1} +b_{2} \right ) \textit {\_Z}^{2}+\left (b_{1} a +b_{2} a \right ) \textit {\_Z} +b_{1} b_{2} , \operatorname {index} &=3\right ) t}+c_{6} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (b_{1} +b_{2} \right ) \textit {\_Z}^{2}+\left (b_{1} a +b_{2} a \right ) \textit {\_Z} +b_{1} b_{2} , \operatorname {index} &=4\right ) t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.475 (sec). Leaf size: 3386
DSolve[{x''[t]+a*(x'[t]-y'[t])+b1*x[t]==c1*Exp[I*\[Omega]*t],y''[t]+a*(y'[t]-x'[t])+b2*y[t]==c2*Exp[I*\[Omega]*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Too large to display