Internal problem ID [11578]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 4, Linear Systems. Exercises page 244
Problem number: 6.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }&=3 x+2 y \left (t \right )+3\\ y^{\prime }\left (t \right )&=7 x+5 y \left (t \right )+2 t \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 91
dsolve([diff(x(t),t)=3*x(t)+2*y(t)+3,diff(y(t),t)=7*x(t)+5*y(t)+2*t],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = \frac {{\mathrm e}^{\left (4+\sqrt {15}\right ) t} c_{2} \sqrt {15}}{7}-\frac {{\mathrm e}^{-\left (-4+\sqrt {15}\right ) t} c_{1} \sqrt {15}}{7}-\frac {{\mathrm e}^{\left (4+\sqrt {15}\right ) t} c_{2}}{7}-\frac {{\mathrm e}^{-\left (-4+\sqrt {15}\right ) t} c_{1}}{7}+4 t +17 \] \[ y \left (t \right ) = {\mathrm e}^{\left (4+\sqrt {15}\right ) t} c_{2} +{\mathrm e}^{-\left (-4+\sqrt {15}\right ) t} c_{1} -6 t -25 \]
✓ Solution by Mathematica
Time used: 2.783 (sec). Leaf size: 178
DSolve[{x'[t]==3*x[t]+2*y[t],y'[t]==7*x[t]+5*y[t]+2*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{30} e^{-\left (\left (\sqrt {15}-4\right ) t\right )} \left (120 e^{\left (\sqrt {15}-4\right ) t} (t+8)+\left (2 \sqrt {15} c_2-\left (\sqrt {15}-15\right ) c_1\right ) e^{2 \sqrt {15} t}+\left (15+\sqrt {15}\right ) c_1-2 \sqrt {15} c_2\right ) y(t)\to \frac {1}{30} e^{-\left (\left (\sqrt {15}-4\right ) t\right )} \left (-60 e^{\left (\sqrt {15}-4\right ) t} (3 t+23)+\left (7 \sqrt {15} c_1+\left (15+\sqrt {15}\right ) c_2\right ) e^{2 \sqrt {15} t}-7 \sqrt {15} c_1-\left (\sqrt {15}-15\right ) c_2\right ) \end{align*}