20.20.2 problem 2

Internal problem ID [3892]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 9, First order linear systems. Section 9.11 (Chapter review), page 665
Problem number : 2
Date solved : Monday, January 27, 2025 at 08:04:08 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x_{1} \left (t \right )&=t \cot \left (t^{2}\right ) x_{1} \left (t \right )+\frac {t \cos \left (t^{2}\right ) x_{3} \left (t \right )}{2}\\ \frac {d}{d t}x_{2} \left (t \right )&=\frac {x_{2} \left (t \right )}{t}-x_{3} \left (t \right )+2-t \sin \left (t \right )\\ \frac {d}{d t}x_{3} \left (t \right )&=\csc \left (t^{2}\right ) x_{1} \left (t \right )+x_{2} \left (t \right )-x_{3} \left (t \right )+1-t \cos \left (t \right ) \end{align*}

✗ Solution by Maple

dsolve([diff(x__1(t),t)=t*cot(t^2)*x__1(t)+t*cos(t^2)/2*x__3(t),diff(x__2(t),t)=1/t*x__2(t)-x__3(t)+(2-t*sin(t)),diff(x__3(t),t)=csc(t^2)*x__1(t)+x__2(t)-x__3(t)+(1-t*cos(t))],singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{D[x1[t],t]==t*Cot[t^2]*x1[t]+t*Cos[t^2]*x3[t],D[x2[t],t]==1/t*x2[t]-x3[t]+(2-t*Sin[t]),D[x3[t],t]==Csc[t^2]*x1[t]+x2[t]-x3[t]+(1-t*Cos[t])},{x1[t],x2[t],x3[t]},t,IncludeSingularSolutions -> True]
 

Not solved