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 : Monday, January 27, 2025 at 03:46:04 PM
CAS classification : system_of_ODEs

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

With initial conditions

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

✗ Solution by Maple

dsolve([diff(x(t),t) = t*y(t)+1, diff(y(t),t) = -t*x(t)+y(t), x(0) = 0, y(0) = -1], singsol=all)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

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

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

Not solved