Internal problem ID [9472]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1893.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} a_{1} x^{\prime \prime }\relax (t )+b_{1} x^{\prime }\relax (t )+c_{1} x \relax (t )-A y^{\prime }\relax (t )&=B \,{\mathrm e}^{i \omega t}\\ a_{2} y^{\prime \prime }\relax (t )+b_{2} y^{\prime }\relax (t )+c_{2} y \relax (t )+A x^{\prime }\relax (t )&=0 \end {align*}
✓ Solution by Maple
Time used: 0.954 (sec). Leaf size: 1601
dsolve({a__1*diff(x(t),t,t)+b__1*diff(x(t),t)+c__1*x(t)-A*diff(y(t),t)=B*exp(I*omega*t),a__2*diff(y(t),t,t)+b__2*diff(y(t),t)+c__2*y(t)+A*diff(x(t),t)=0},{x(t), y(t)}, singsol=all)
\[ \text {Expression too large to display} \] \[ y \relax (t ) = \frac {i B A \,{\mathrm e}^{i \omega t} \omega }{-a_{2} a_{1} \omega ^{4}+i a_{1} b_{2} \omega ^{3}+i b_{1} a_{2} \omega ^{3}+A^{2} \omega ^{2}+a_{1} c_{2} \omega ^{2}+a_{2} c_{1} \omega ^{2}+b_{2} b_{1} \omega ^{2}-i c_{2} b_{1} \omega -i b_{2} c_{1} \omega -c_{1} c_{2}}+c_{1} {\mathrm e}^{\RootOf \left (a_{1} a_{2} \textit {\_Z}^{4}+\left (a_{1} b_{2} +b_{1} a_{2} \right ) \textit {\_Z}^{3}+\left (A^{2}+a_{1} c_{2} +a_{2} c_{1} +b_{2} b_{1} \right ) \textit {\_Z}^{2}+\left (c_{2} b_{1} +b_{2} c_{1} \right ) \textit {\_Z} +c_{1} c_{2} , \mathit {index} =1\right ) t}+c_{2} {\mathrm e}^{\RootOf \left (a_{1} a_{2} \textit {\_Z}^{4}+\left (a_{1} b_{2} +b_{1} a_{2} \right ) \textit {\_Z}^{3}+\left (A^{2}+a_{1} c_{2} +a_{2} c_{1} +b_{2} b_{1} \right ) \textit {\_Z}^{2}+\left (c_{2} b_{1} +b_{2} c_{1} \right ) \textit {\_Z} +c_{1} c_{2} , \mathit {index} =2\right ) t}+c_{3} {\mathrm e}^{\RootOf \left (a_{1} a_{2} \textit {\_Z}^{4}+\left (a_{1} b_{2} +b_{1} a_{2} \right ) \textit {\_Z}^{3}+\left (A^{2}+a_{1} c_{2} +a_{2} c_{1} +b_{2} b_{1} \right ) \textit {\_Z}^{2}+\left (c_{2} b_{1} +b_{2} c_{1} \right ) \textit {\_Z} +c_{1} c_{2} , \mathit {index} =3\right ) t}+c_{4} {\mathrm e}^{\RootOf \left (a_{1} a_{2} \textit {\_Z}^{4}+\left (a_{1} b_{2} +b_{1} a_{2} \right ) \textit {\_Z}^{3}+\left (A^{2}+a_{1} c_{2} +a_{2} c_{1} +b_{2} b_{1} \right ) \textit {\_Z}^{2}+\left (c_{2} b_{1} +b_{2} c_{1} \right ) \textit {\_Z} +c_{1} c_{2} , \mathit {index} =4\right ) t} \]
✓ Solution by Mathematica
Time used: 53.81 (sec). Leaf size: 149009
DSolve[{a1*x''[t]+b1*x'[t]+c1*x[t]-A*t'[t]==B*Exp[I*\[Omega]*t],a2*y''[t]+b2*y'[t]+c2*y[t]+A*x'[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Too large to display