Internal problem ID [9474]
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 }\relax (t )+\mathit {b11} x^{\prime }\relax (t )+\mathit {c11} x \relax (t )+\mathit {a12} y^{\prime \prime }\relax (t )+\mathit {b12} y^{\prime }\relax (t )+\mathit {c12} y \relax (t )&=0\\ \mathit {a21} x^{\prime \prime }\relax (t )+\mathit {b21} x^{\prime }\relax (t )+\mathit {c21} x \relax (t )+\mathit {a22} y^{\prime \prime }\relax (t )+\mathit {b22} y^{\prime }\relax (t )+\mathit {c22} y \relax (t )&=0 \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 1187
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},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\RootOf \left (\left (\mathit {a11} \mathit {a22} -\mathit {a21} \mathit {a12} \right ) \textit {\_Z}^{4}+\left (\mathit {a11} \mathit {b22} -\mathit {a12} \mathit {b21} -\mathit {a21} \mathit {b12} +\mathit {a22} \mathit {b11} \right ) \textit {\_Z}^{3}+\left (\mathit {a11} \mathit {c22} -\mathit {a12} \mathit {c21} -\mathit {a21} \mathit {c12} +\mathit {a22} \mathit {c11} +\mathit {b11} \mathit {b22} -\mathit {b12} \mathit {b21} \right ) \textit {\_Z}^{2}+\left (\mathit {b11} \mathit {c22} -\mathit {c21} \mathit {b12} -\mathit {b21} \mathit {c12} +\mathit {b22} \mathit {c11} \right ) \textit {\_Z} +\mathit {c11} \mathit {c22} -\mathit {c21} \mathit {c12} , \mathit {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}} \] \[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.119 (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