Internal problem ID [7388]
Book: First order enumerated odes
Section: section 2 (system of first order ode’s)
Problem number: 2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )-2 y \left (t \right )+t -{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=3 x \left (t \right )+5 y \left (t \right )-t +2 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 95
dsolve([2*diff(x(t),t)+diff(y(t),t)-x(t)=y(t)+t,diff(x(t),t)+diff(y(t),t)=2*x(t)+3*y(t)+exp(t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{\left (2+\sqrt {3}\right ) t} c_{2} +{\mathrm e}^{-\left (-2+\sqrt {3}\right ) t} c_{1} -3 t -11 \\ y \left (t \right ) &= -\frac {{\mathrm e}^{\left (2+\sqrt {3}\right ) t} c_{2} \sqrt {3}}{2}+\frac {{\mathrm e}^{-\left (-2+\sqrt {3}\right ) t} c_{1} \sqrt {3}}{2}-\frac {3 \,{\mathrm e}^{\left (2+\sqrt {3}\right ) t} c_{2}}{2}-\frac {3 \,{\mathrm e}^{-\left (-2+\sqrt {3}\right ) t} c_{1}}{2}-\frac {{\mathrm e}^{t}}{2}+2 t +7 \\ \end{align*}
✓ Solution by Mathematica
Time used: 10.209 (sec). Leaf size: 174
DSolve[{2*x'[t]+y'[t]-x[t]==y[t]+t,x'[t]+y'[t]==2*x[t]+3*y[t]+Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{6} e^{-\left (\left (\sqrt {3}-2\right ) t\right )} \left (-6 e^{\left (\sqrt {3}-2\right ) t} (3 t+11)+\left (-3 \left (\sqrt {3}-1\right ) c_1-2 \sqrt {3} c_2\right ) e^{2 \sqrt {3} t}+3 \left (1+\sqrt {3}\right ) c_1+2 \sqrt {3} c_2\right ) \\ y(t)\to \frac {1}{2} \left (4 t-e^t+\left (-\sqrt {3} c_1-\sqrt {3} c_2+c_2\right ) e^{-\left (\left (\sqrt {3}-2\right ) t\right )}+\left (\sqrt {3} c_1+\left (1+\sqrt {3}\right ) c_2\right ) e^{\left (2+\sqrt {3}\right ) t}+14\right ) \\ \end{align*}