Internal problem ID [9452]
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 }\relax (t )&=-2 x \relax (t )-y \relax (t )+7 t -9 \,{\mathrm e}^{t}\\ y^{\prime }\relax (t )&=-4 x \relax (t )-5 y \relax (t )-3 t +4 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.083 (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)
\[ x \relax (t ) = {\mathrm e}^{-t} c_{2}+c_{1} {\mathrm e}^{-6 t}-\frac {29 \,{\mathrm e}^{t}}{7}+\frac {19 t}{3}-\frac {56}{9} \] \[ y \relax (t ) = -{\mathrm e}^{-t} c_{2}+4 c_{1} {\mathrm e}^{-6 t}+\frac {24 \,{\mathrm e}^{t}}{7}+\frac {55}{9}-\frac {17 t}{3} \]
✓ Solution by Mathematica
Time used: 0.111 (sec). Leaf size: 102
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} (c_2-4 c_1) 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*}