Internal problem ID [11939]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 7, Systems of linear differential equations. Section 7.1. Exercises page
277
Problem number: 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 t^{2}-6 y \left (t \right )-2 t -1\\ y^{\prime }\left (t \right )&=-t^{2}+x \left (t \right )+y \left (t \right )+2 t +1 \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 116
dsolve([diff(x(t),t)+diff(y(t),t)-x(t)+5*y(t)=t^2,diff(x(t),t)+2*diff(y(t),t)-2*x(t)+4*y(t)=2*t+1],singsol=all)
\begin{align*} x \left (t \right ) &= {\mathrm e}^{\frac {t}{2}} \sin \left (\frac {\sqrt {23}\, t}{2}\right ) c_{2} +{\mathrm e}^{\frac {t}{2}} \cos \left (\frac {\sqrt {23}\, t}{2}\right ) c_{1} +\frac {2 t^{2}}{3}-\frac {7 t}{9}-\frac {41}{27} \\ y \left (t \right ) &= \frac {t^{2}}{3}-\frac {{\mathrm e}^{\frac {t}{2}} \sin \left (\frac {\sqrt {23}\, t}{2}\right ) c_{2}}{12}-\frac {{\mathrm e}^{\frac {t}{2}} \sqrt {23}\, \cos \left (\frac {\sqrt {23}\, t}{2}\right ) c_{2}}{12}-\frac {{\mathrm e}^{\frac {t}{2}} \cos \left (\frac {\sqrt {23}\, t}{2}\right ) c_{1}}{12}+\frac {{\mathrm e}^{\frac {t}{2}} \sqrt {23}\, \sin \left (\frac {\sqrt {23}\, t}{2}\right ) c_{1}}{12}-\frac {5 t}{9}-\frac {1}{27} \\ \end{align*}
✓ Solution by Mathematica
Time used: 11.178 (sec). Leaf size: 143
DSolve[{x'[t]+y'[t]-x[t]+5*y[t]==t^2,x'[t]+2*y'[t]-2*x[t]+4*y[t]==2*t+1},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{27} \left (18 t^2-21 t-41\right )+c_1 e^{t/2} \cos \left (\frac {\sqrt {23} t}{2}\right )-\frac {(c_1+12 c_2) e^{t/2} \sin \left (\frac {\sqrt {23} t}{2}\right )}{\sqrt {23}} \\ y(t)\to \frac {1}{27} \left (9 t^2-15 t-1\right )+c_2 e^{t/2} \cos \left (\frac {\sqrt {23} t}{2}\right )+\frac {(2 c_1+c_2) e^{t/2} \sin \left (\frac {\sqrt {23} t}{2}\right )}{\sqrt {23}} \\ \end{align*}