60.9.14 problem 1869

Internal problem ID [11868]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1869
Date solved : Monday, January 27, 2025 at 11:44:02 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )+2 x \left (t \right )+y \left (t \right )&={\mathrm e}^{2 t}+t\\ \frac {d}{d t}x \left (t \right )+\frac {d}{d t}y \left (t \right )-x \left (t \right )+3 y \left (t \right )&={\mathrm e}^{t}-1 \end{align*}

✓ Solution by Maple

Time used: 0.075 (sec). Leaf size: 50

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],singsol=all)
 

\begin{align*} x \left (t \right ) &= \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 \left (t \right ) &= -\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} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.193 (sec). Leaf size: 84

DSolve[{D[x[t],t]+D[y[t],t]+2*x[t]+y[t]==Exp[2*t]+t,D[x[t],t]+D[y[t],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*}