Internal problem ID [10261]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 9, system of higher order odes
Problem number: 1939.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x_{1}^{\prime }\left (t \right )&=\frac {x_{4} \left (t \right ) \sin \left (x_{3} \left (t \right )\right )}{\sin \left (x_{2} \left (t \right )\right )}+\frac {x_{5} \left (t \right ) \cos \left (x_{3} \left (t \right )\right )}{\sin \left (x_{2} \left (t \right )\right )}\\ x_{2}^{\prime }\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 )\\ x_{3}^{\prime }\left (t \right )&=-\frac {\cos \left (x_{2} \left (t \right )\right ) x_{4} \left (t \right ) \sin \left (x_{3} \left (t \right )\right )}{\sin \left (x_{2} \left (t \right )\right )}-\frac {\cos \left (x_{2} \left (t \right )\right ) \cos \left (x_{3} \left (t \right )\right ) x_{5} \left (t \right )}{\sin \left (x_{2} \left (t \right )\right )}+a\\ x_{4}^{\prime }\left (t \right )&=-m \sin \left (x_{2} \left (t \right )\right ) \cos \left (x_{3} \left (t \right )\right )-a x_{5} \left (t \right ) \lambda +a x_{5} \left (t \right )\\ x_{5}^{\prime }\left (t \right )&=m \sin \left (x_{2} \left (t \right )\right ) \sin \left (x_{3} \left (t \right )\right )+a x_{4} \left (t \right ) \lambda -a x_{4} \left (t \right ) \end {align*}
✗ Solution by Maple
dsolve([diff(x__1(t),t)*sin(x__2(t))=x__4(t)*sin(x__3(t))+x__5(t)*cos(x__3(t)),diff(x__2(t),t)= x__4(t)*cos(x__3(t))-x__5(t)*sin(x__3(t)),diff(x__3(t),t)+diff(x__1(t),t)*cos(x__2(t))= a,diff(x__4(t),t)-(1-lambda)*a*x__5(t)= -m*sin(x__2(t))*cos(x__3(t)),diff(x__5(t),t)+(1-lambda)*a*x__4(t)= m*sin(x__2(t))*sin(x__3(t))],singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{x1'[t]*Sin[x2[t]]==x4[t]*Sin[x3[t]]+x5[t]*Cos[x3[t]],x2'[t]==x4[t]*Cos[x3[t]]-x5[t]*Sin[x3[t]],x3'[t]+x1'[t]*Cos[x2[t]]== a,x4'[t]-(1-\[Lambda])*a*x5[t]== -m*Sin[x2[t]]*Cos[x3[t]],x5'[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