Internal problem ID [6720]
Book: DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL,
WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th
edition.
Section: CHAPTER 8 SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS.
EXERCISES 8.1. Page 332
Problem number: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=t \,{\mathrm e}^{4 t}+4 \sin \left (t \right )-4 \,{\mathrm e}^{4 t}-7 y+3 x \left (t \right )\\ y^{\prime }&=2 t \,{\mathrm e}^{4 t}+{\mathrm e}^{4 t}+8 \sin \left (t \right )+y+x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 1.156 (sec). Leaf size: 134
dsolve([diff(x(t),t)=3*x(t)-7*y(t)+4*sin(t)+(t-4)*exp(4*t),diff(y(t),t)=x(t)+y(t)+8*sin(t)+(2*t+1)*exp(4*t)],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{2 t} \sin \left (\sqrt {6}\, t \right ) c_{2} +{\mathrm e}^{2 t} \cos \left (\sqrt {6}\, t \right ) c_{1} -\frac {11 \,{\mathrm e}^{4 t} t}{10}-\frac {34 \,{\mathrm e}^{4 t}}{25}-\frac {204 \cos \left (t \right )}{97}-\frac {556 \sin \left (t \right )}{97} \\ y \left (t \right ) &= \frac {3 \,{\mathrm e}^{4 t} t}{10}+\frac {{\mathrm e}^{2 t} \sqrt {6}\, \sin \left (\sqrt {6}\, t \right ) c_{1}}{7}-\frac {{\mathrm e}^{2 t} \sqrt {6}\, \cos \left (\sqrt {6}\, t \right ) c_{2}}{7}-\frac {11 \,{\mathrm e}^{4 t}}{50}+\frac {{\mathrm e}^{2 t} \sin \left (\sqrt {6}\, t \right ) c_{2}}{7}+\frac {{\mathrm e}^{2 t} \cos \left (\sqrt {6}\, t \right ) c_{1}}{7}-\frac {8 \cos \left (t \right )}{97}-\frac {212 \sin \left (t \right )}{97} \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.331 (sec). Leaf size: 190
DSolve[{x'[t]==3*x[t]-7*y[t]+4*Sin[t]+(t-4)*Exp[4*t],y'[t]==x[t]+y[t]+8*Sin[t]+(2*t+1)*Exp[4*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {11}{10} e^{4 t} t-\frac {34 e^{4 t}}{25}-\frac {556 \sin (t)}{97}-\frac {204 \cos (t)}{97}+c_1 e^{2 t} \cos \left (\sqrt {6} t\right )+\frac {c_1 e^{2 t} \sin \left (\sqrt {6} t\right )}{\sqrt {6}}-\frac {7 c_2 e^{2 t} \sin \left (\sqrt {6} t\right )}{\sqrt {6}} \\ y(t)\to \frac {3}{10} e^{4 t} t-\frac {11 e^{4 t}}{50}-\frac {212 \sin (t)}{97}-\frac {8 \cos (t)}{97}+c_2 e^{2 t} \cos \left (\sqrt {6} t\right )+\frac {c_1 e^{2 t} \sin \left (\sqrt {6} t\right )}{\sqrt {6}}-\frac {c_2 e^{2 t} \sin \left (\sqrt {6} t\right )}{\sqrt {6}} \\ \end{align*}