Internal problem ID [9448]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1869.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\relax (t )+y^{\prime }\relax (t )-x \relax (t )+3 y \relax (t )&={\mathrm e}^{t}-1\\ x^{\prime }\relax (t )+y^{\prime }\relax (t )+2 x \relax (t )+y \relax (t )&={\mathrm e}^{2 t}+t \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 51
dsolve({diff(x(t),t)+diff(y(t),t)+2*x(t)+y(t)=exp(2*t)+t,diff(x(t),t)+diff(y(t),t)-x(t)+3*y(t)=exp(t)-1},{x(t), y(t)}, singsol=all)
\[ x \relax (t ) = \frac {3 t}{7}-\frac {1}{49}-\frac {{\mathrm e}^{t}}{6}+\frac {5 \,{\mathrm e}^{2 t}}{17}+{\mathrm e}^{-\frac {7 t}{5}} c_{1} \] \[ y \relax (t ) = -\frac {{\mathrm e}^{2 t}}{17}+\frac {t}{7}-\frac {26}{49}+\frac {{\mathrm e}^{t}}{4}+\frac {3 \,{\mathrm e}^{-\frac {7 t}{5}} c_{1}}{2} \]
✓ Solution by Mathematica
Time used: 0.113 (sec). Leaf size: 84
DSolve[{x'[t]+y'[t]+2*x[t]+y[t]==Exp[2*t]+t,x'[t]+y'[t]-x[t]+3*y[t]==Exp[t]-1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {3 t}{7}-\frac {e^t}{6}+\frac {5 e^{2 t}}{17}+\frac {5}{72} c_1 e^{-7 t/5}-\frac {1}{49} \\ y(t)\to \frac {t}{7}+\frac {e^t}{4}-\frac {e^{2 t}}{17}+\frac {5}{48} c_1 e^{-7 t/5}-\frac {26}{49} \\ \end{align*}