Internal problem ID [7387]
Book: First order enumerated odes
Section: section 2 (system of first order ode’s)
Problem number: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=x \left (t \right )+y \left (t \right )+t\\ x^{\prime }\left (t \right )+y^{\prime }\left (t \right )&=2 x \left (t \right )+3 y \left (t \right )+{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 31
dsolve([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 ) &= -3 t -2+c_{1} {\mathrm e}^{t} \\ y \left (t \right ) &= 2 t +1-\frac {c_{1} {\mathrm e}^{t}}{2}-\frac {{\mathrm e}^{t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.042 (sec). Leaf size: 37
DSolve[{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 -3 t+(1+2 c_1) e^t-2 \\ y(t)\to 2 t-(1+c_1) e^t+1 \\ \end{align*}