Internal problem ID [9446]
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 }\relax (t )&=t^{2}-y \relax (t )-6 t -1\\ y^{\prime }\relax (t )&=-3 t^{2}+x \relax (t )+3 t +1 \end {align*}
✓ Solution by Maple
Time used: 0.078 (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},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = \sin \relax (t ) c_{2}+\cos \relax (t ) c_{1}+3 t^{2}-t -13 \] \[ y \relax (t ) = t^{2}-c_{2} \cos \relax (t )+c_{1} \sin \relax (t )-12 t \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 44
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 t (3 t-1)+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*}