Internal problem ID [10205]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 8, system of first order odes
Problem number: 1873.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-2 x \left (t \right )-y \left (t \right )+7 t -9 \,{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=-4 x \left (t \right )-5 y \left (t \right )-3 t +4 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.125 (sec). Leaf size: 52
dsolve([4*diff(x(t),t)+9*diff(y(t),t)+44*x(t)+49*y(t)=t,3*diff(x(t),t)+7*diff(y(t),t)+34*x(t)+38*y(t)=exp(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = -c_{2} {\mathrm e}^{-t}+\frac {{\mathrm e}^{-6 t} c_{1}}{4}-\frac {29 \,{\mathrm e}^{t}}{7}-\frac {56}{9}+\frac {19 t}{3} \] \[ y \left (t \right ) = c_{2} {\mathrm e}^{-t}+{\mathrm e}^{-6 t} c_{1} +\frac {24 \,{\mathrm e}^{t}}{7}-\frac {17 t}{3}+\frac {55}{9} \]
✓ Solution by Mathematica
Time used: 0.232 (sec). Leaf size: 104
DSolve[{4*x'[t]+9*y'[t]+44*x[t]+49*y[t]==t,3*x'[t]+7*y'[t]+34*x[t]+38*y[t]==Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{9} (57 t-56)-\frac {29 e^t}{7}+\frac {1}{5} (4 c_1-c_2) e^{-t}+\frac {1}{5} (c_1+c_2) e^{-6 t} y(t)\to \frac {1}{9} (55-51 t)+\frac {24 e^t}{7}+\frac {1}{5} (c_2-4 c_1) e^{-t}+\frac {4}{5} (c_1+c_2) e^{-6 t} \end{align*}