Internal problem ID [7389]
Book: First order enumerated odes
Section: section 2 (system of first order ode’s)
Problem number: 3.
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 +\sin \left (t \right )+\cos \left (t \right )\\ 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: 0.078 (sec). Leaf size: 45
dsolve([diff(x(t),t)+diff(y(t),t)-x(t)=y(t)+t+sin(t)+cos(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 ) &= -\sin \left (t \right )-3 \cos \left (t \right )+c_{1} {\mathrm e}^{t}-3 t -2 \\ y \left (t \right ) &= \sin \left (t \right )+2 \cos \left (t \right )-\frac {c_{1} {\mathrm e}^{t}}{2}+2 t +1-\frac {{\mathrm e}^{t}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 54
DSolve[{x'[t]+y'[t]-x[t]==y[t]+t+Sin[t]+Cos[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+e^t-\sin (t)-3 \cos (t)+2 c_1 e^t-2 \\ y(t)\to 2 t-e^t+\sin (t)+2 \cos (t)-c_1 e^t+1 \\ \end{align*}