Internal problem ID [14035]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 38. Systems of differential equations. A starting point. Additional Exercises.
page 786
Problem number: 38.10 (i).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=4 x \left (t \right )+3 y \left (t \right )-6 \,{\mathrm e}^{3 t}\\ y^{\prime }\left (t \right )&=x \left (t \right )+6 y \left (t \right )+2 \,{\mathrm e}^{3 t} \end {align*}
With initial conditions \[ [x \left (0\right ) = 4, y \left (0\right ) = 0] \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 44
dsolve([diff(x(t),t) = 4*x(t)+3*y(t)-6*exp(3*t), diff(y(t),t) = x(t)+6*y(t)+2*exp(3*t), x(0) = 4, y(0) = 0], singsol=all)
\begin{align*} x \left (t \right ) &= 3 \,{\mathrm e}^{3 t}+{\mathrm e}^{7 t}-6 \,{\mathrm e}^{3 t} t \\ y \left (t \right ) &= -{\mathrm e}^{3 t}+{\mathrm e}^{7 t}+2 \,{\mathrm e}^{3 t} t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 50
DSolve[{x'[t]==4*x[t]+3*y[t]+6*Exp[3*t],y'[t]==x[t]+6*y[t]+2*Exp[3*t]},{x[0]==4,y[0]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{4} e^{3 t} \left (12 t+7 e^{4 t}+9\right ) \\ y(t)\to \frac {1}{4} e^{3 t} \left (-4 t+7 e^{4 t}-7\right ) \\ \end{align*}