Internal problem ID [10190]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1867.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=t^{2}-y \left (t \right )-6 t -1\\ y^{\prime }\left (t \right )&=-3 t^{2}+x \left (t \right )+3 t +1 \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve([diff(x(t),t)+y(t)-t^2+6*t+1=0,diff(y(t),t)-x(t)=-3*t^2+3*t+1],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )+3 t^{2}-t -13 \\ y \left (t \right ) &= t^{2}-c_{2} \cos \left (t \right )+c_{1} \sin \left (t \right )-12 t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.255 (sec). Leaf size: 45
DSolve[{x'[t]+y[t]-t^2+6*t+1==0,y'[t]-x[t]==-3*t^2+3*t+1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to 3 t^2-t+c_1 \cos (t)-c_2 \sin (t)-13 \\ y(t)\to (t-12) t+c_2 \cos (t)+c_1 \sin (t) \\ \end{align*}