Internal problem ID [9473]
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 }\relax (t )+a \left (x^{\prime }\relax (t )-y^{\prime }\relax (t )\right )+b_{1} x \relax (t )&=c_{1} {\mathrm e}^{i \omega t}\\ y^{\prime \prime }\relax (t )+a \left (y^{\prime }\relax (t )-x^{\prime }\relax (t )\right )+b_{2} y \relax (t )&=c_{2} {\mathrm e}^{i \omega t} \end {align*}
✓ Solution by Maple
Time used: 0.656 (sec). Leaf size: 2555
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)},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = \frac {i {\mathrm e}^{i \omega t} a c_{1} \omega +i {\mathrm e}^{i \omega t} a c_{2} \omega -\omega ^{2} c_{1} {\mathrm e}^{i \omega t}+c_{1} {\mathrm e}^{i \omega t} b_{2}}{-2 i a \,\omega ^{3}+i a b_{1} \omega +i a b_{2} \omega +\omega ^{4}-b_{1} \omega ^{2}-b_{2} \omega ^{2}+b_{2} b_{1}}+c_{1} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (b_{1} +b_{2} \right ) \textit {\_Z}^{2}+\left (b_{1} a +a b_{2} \right ) \textit {\_Z} +b_{2} b_{1} , \mathit {index} =1\right ) t}+c_{2} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (b_{1} +b_{2} \right ) \textit {\_Z}^{2}+\left (b_{1} a +a b_{2} \right ) \textit {\_Z} +b_{2} b_{1} , \mathit {index} =2\right ) t}+c_{3} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (b_{1} +b_{2} \right ) \textit {\_Z}^{2}+\left (b_{1} a +a b_{2} \right ) \textit {\_Z} +b_{2} b_{1} , \mathit {index} =3\right ) t}+c_{4} {\mathrm e}^{\RootOf \left (\textit {\_Z}^{4}+2 a \,\textit {\_Z}^{3}+\left (b_{1} +b_{2} \right ) \textit {\_Z}^{2}+\left (b_{1} a +a b_{2} \right ) \textit {\_Z} +b_{2} b_{1} , \mathit {index} =4\right ) t} \] \[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.3 (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