60.10.26 problem 1939

Internal problem ID [11937]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1939
Date solved : Monday, January 27, 2025 at 11:47:27 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*}

✗ 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: 0.000 (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