Internal problem ID [7291]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 67.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+2 y \left (t \right )+2 t +1\\ y^{\prime }\left (t \right )&=5 x \left (t \right )+y \left (t \right )+3 t -1 \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 68
dsolve([diff(x(t),t)=x(t)+2*y(t)+2*t+1,diff(y(t),t)=5*x(t)+y(t)+3*t-1],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{\left (1+\sqrt {10}\right ) t} c_{2} +{\mathrm e}^{-\left (-1+\sqrt {10}\right ) t} c_{1} -\frac {4 t}{9}+\frac {17}{81} \\ y \left (t \right ) &= \frac {{\mathrm e}^{\left (1+\sqrt {10}\right ) t} c_{2} \sqrt {10}}{2}-\frac {{\mathrm e}^{-\left (-1+\sqrt {10}\right ) t} c_{1} \sqrt {10}}{2}-\frac {7 t}{9}-\frac {67}{81} \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.731 (sec). Leaf size: 158
DSolve[{x'[t]==x[t]+2*y[t]+2*t+1,y'[t]==5*x[t]+y[t]+3*t-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{810} e^{t-\sqrt {10} t} \left (e^{\left (\sqrt {10}-1\right ) t} (170-360 t)+81 \left (5 c_1+\sqrt {10} c_2\right ) e^{2 \sqrt {10} t}+81 \left (5 c_1-\sqrt {10} c_2\right )\right ) \\ y(t)\to \frac {1}{324} e^{t-\sqrt {10} t} \left (-4 e^{\left (\sqrt {10}-1\right ) t} (63 t+67)+81 \left (\sqrt {10} c_1+2 c_2\right ) e^{2 \sqrt {10} t}-81 \left (\sqrt {10} c_1-2 c_2\right )\right ) \\ \end{align*}