50.30.2 problem 2

Internal problem ID [8211]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 10. Systems of First-Order Equations. Section B. Challenge Problems. Page 401
Problem number : 2
Date solved : Wednesday, March 05, 2025 at 05:32:19 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )&=t y \left (t \right )+1\\ \frac {d}{d t}y \left (t \right )&=-t x \left (t \right )+y \left (t \right ) \end{align*}

With initial conditions

\begin{align*} x \left (0\right ) = 0\\ y \left (0\right ) = -1 \end{align*}

✗ Maple

ode:=[diff(x(t),t) = t*y(t)+1, diff(y(t),t) = -t*x(t)+y(t)]; 
ic:=x(0) = 0y(0) = -1; 
dsolve([ode,ic]);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={D[x[t],t]==x[t]*y[t]+1,D[y[t],t]==-x[t]+y[t]}; 
ic={x[0]==2,y[0]==-1}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-t*y(t) + Derivative(x(t), t) - 1,0),Eq(t*x(t) - y(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

NotImplementedError :