90.33.4 problem 4

Internal problem ID [25478]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 9. Linear Systems of Differential Equations. Exercises at page 645
Problem number : 4
Date solved : Sunday, October 12, 2025 at 05:55:39 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}y_{1} \left (t \right )&=t \sin \left (y_{1} \left (t \right )\right )-y_{2} \left (t \right )\\ \frac {d}{d t}y_{2} \left (t \right )&=y_{1} \left (t \right )+t \cos \left (y_{2} \left (t \right )\right ) \end{align*}

✓ Maple. Time used: 2.651 (sec). Leaf size: 58

ode:=[diff(y__1(t),t) = t*sin(y__1(t))-y__2(t), diff(y__2(t),t) = y__1(t)+t*cos(y__2(t))]; 
dsolve(ode);
 

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

✗ Mathematica

ode={D[y1[t],t]==t*Sin[y1[t]]-y2[t],D[y2[t],t]==y1[t]+t*Cos[y2[t]]}; 
ic={}; 
DSolve[{ode,ic},{y1[t],y2[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
y1 = Function("y1") 
y2 = Function("y2") 
ode=[Eq(-t*sin(y1(t)) + y2(t) + Derivative(y1(t), t),0),Eq(-t*cos(y2(t)) - y1(t) + Derivative(y2(t), t),0)] 
ics = {} 
dsolve(ode,func=[y1(t),y2(t)],ics=ics)
 

NotImplementedError :