60.9.40 problem 1895
Internal
problem
ID
[11894]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
8,
system
of
first
order
odes
Problem
number
:
1895
Date
solved
:
Tuesday, January 28, 2025 at 06:24:03 PM
CAS
classification
:
system_of_ODEs
\begin{align*} \operatorname {a11} \left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right )+\operatorname {b11} \left (\frac {d}{d t}x \left (t \right )\right )+\operatorname {c11} x \left (t \right )+\operatorname {a12} \left (\frac {d^{2}}{d t^{2}}y \left (t \right )\right )+\operatorname {b12} \left (\frac {d}{d t}y \left (t \right )\right )+\operatorname {c12} y \left (t \right )&=0\\ \operatorname {a21} \left (\frac {d^{2}}{d t^{2}}x \left (t \right )\right )+\operatorname {b21} \left (\frac {d}{d t}x \left (t \right )\right )+\operatorname {c21} x \left (t \right )+\operatorname {a22} \left (\frac {d^{2}}{d t^{2}}y \left (t \right )\right )+\operatorname {b22} \left (\frac {d}{d t}y \left (t \right )\right )+\operatorname {c22} y \left (t \right )&=0 \end{align*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 1186
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*}
x \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 {b22} \operatorname {a11} -\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}} \\
\text {Expression too large to display} \\
\end{align*}
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 7517
DSolve[{a11*D[x[t],{t,2}]+b11*D[x[t],t]+c11*x[t]+a12*D[y[t],{t,2}]+b12*D[y[t],t]+c12*y[t]==0,a21*D[x[t],{t,2}]+b21*D[x[t],t]+c21*x[t]+a22*D[y[t],{t,2}]+b22*D[y[t],t]+c22*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
Too large to display