Internal
problem
ID
[10910]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
9,
system
of
higher
order
odes
Problem
number
:
1939
Date
solved
:
Friday, October 11, 2024 at 12:20:33 PM
CAS
classification
:
system_of_ODEs
\begin{align*} \left (\frac {d}{d t}x_{1} \left (t \right )\right ) \sin \left (x_{2} \left (t \right )\right )&=x_{4} \left (t \right ) \sin \left (x_{3} \left (t \right )\right )+x_{5} \left (t \right ) \cos \left (x_{3} \left (t \right )\right )\\ \frac {d}{d t}x_{2} \left (t \right )&=x_{4} \left (t \right ) \cos \left (x_{3} \left (t \right )\right )-x_{5} \left (t \right ) \sin \left (x_{3} \left (t \right )\right )\\ \frac {d}{d t}x_{3} \left (t \right )+\left (\frac {d}{d t}x_{1} \left (t \right )\right ) \cos \left (x_{2} \left (t \right )\right )&=a\\ \frac {d}{d t}x_{4} \left (t \right )-\left (1-\lambda \right ) a x_{5} \left (t \right )&=-m \sin \left (x_{2} \left (t \right )\right ) \cos \left (x_{3} \left (t \right )\right )\\ \frac {d}{d t}x_{5} \left (t \right )+\left (1-\lambda \right ) a x_{4} \left (t \right )&=m \sin \left (x_{2} \left (t \right )\right ) \sin \left (x_{3} \left (t \right )\right ) \end{align*}
10.26.2 Maple dsolve solution
Solving time : 91.974 (sec)
Leaf size : maple_leaf_size
\[ \text {No solution found} \]
10.26.3 Mathematica DSolve solution
Solving time : 0.0 (sec)
Leaf size : 0
DSolve[{{D[ x1[t],t]*Sin[x2[t]]==x4[t]*Sin[x3[t]]+x5[t]*Cos[x3[t]],D[ x2[t],t]==x4[t]*Cos[x3[t]]-x5[t]*Sin[x3[t]],D[ x3[t],t]+D[ x1[t],t]*Cos[x2[t]]== a,D[ x4[t],t]-(1-\[Lambda])*a*x5[t]== -m*Sin[x2[t]]*Cos[x3[t]],D[ x5[t],t]+(1-\[Lambda])*a*x4[t]== m*Sin[x2[t]]*Sin[x3[t]]},{}},
{x1[t],x2[t],x3[t],x4[t],x5[t]},t,IncludeSingularSolutions->True]
Not solved