Internal problem ID [10218]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1895.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} \mathit {a11} x^{\prime \prime }\left (t \right )+\mathit {b11} x^{\prime }\left (t \right )+\mathit {c11} x \left (t \right )+\mathit {a12} y^{\prime \prime }\left (t \right )+\mathit {b12} y^{\prime }\left (t \right )+\mathit {c12} y \left (t \right )&=0\\ \mathit {a21} x^{\prime \prime }\left (t \right )+\mathit {b21} x^{\prime }\left (t \right )+\mathit {c21} x \left (t \right )+\mathit {a22} y^{\prime \prime }\left (t \right )+\mathit {b22} y^{\prime }\left (t \right )+\mathit {c22} y \left (t \right )&=0 \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 1288
dsolve([a11*diff(x(t),t,t)+b11*diff(x(t),t)+c11*x(t)+a12*diff(y(t),t,t)+b12*diff(y(t),t)+c12*y(t)=0,a21*diff(x(t),t,t)+b21*diff(x(t),t)+c21*x(t)+a22*diff(y(t),t,t)+b22*diff(y(t),t)+c22*y(t)=0],singsol=all)
\begin{align*} \text {Expression too large to display} \\ y \left (t \right ) &= \moverset {4}{\munderset {\textit {\_a} &=1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (\left (\operatorname {a11} \operatorname {a22} -\operatorname {a12} \operatorname {a21} \right ) \textit {\_Z}^{4}+\left (\operatorname {a11} \operatorname {b22} -\operatorname {a12} \operatorname {b21} -\operatorname {a21} \operatorname {b12} +\operatorname {a22} \operatorname {b11} \right ) \textit {\_Z}^{3}+\left (\operatorname {a11} \operatorname {c22} -\operatorname {a12} \operatorname {c21} -\operatorname {a21} \operatorname {c12} +\operatorname {a22} \operatorname {c11} +\operatorname {b11} \operatorname {b22} -\operatorname {b12} \operatorname {b21} \right ) \textit {\_Z}^{2}+\left (\operatorname {b11} \operatorname {c22} -\operatorname {b12} \operatorname {c21} -\operatorname {b21} \operatorname {c12} +\operatorname {b22} \operatorname {c11} \right ) \textit {\_Z} +\operatorname {c11} \operatorname {c22} -\operatorname {c12} \operatorname {c21} , \operatorname {index} &=\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 7517
DSolve[{a11*x''[t]+b11*x'[t]+c11*x[t]+a12*y''[t]+b12*y'[t]+c12*y[t]==0,a21*x''[t]+b21*x'[t]+c21*x[t]+a22*y''[t]+b22*y'[t]+c22*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Too large to display