Internal problem ID [11947]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 7, Systems of linear differential equations. Section 7.3. Exercises page
299
Problem number: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=5 x \left (t \right )+2 y \left (t \right )+5 t\\ y^{\prime }\left (t \right )&=3 x \left (t \right )+4 y \left (t \right )+17 t \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 41
dsolve([diff(x(t),t)=5*x(t)+2*y(t)+5*t,diff(y(t),t)=3*x(t)+4*y(t)+17*t],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{7 t}+c_{1} {\mathrm e}^{2 t}+t +1 \\ y \left (t \right ) &= c_{2} {\mathrm e}^{7 t}-\frac {3 c_{1} {\mathrm e}^{2 t}}{2}-2-5 t \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 84
DSolve[{x'[t]==5*x[t]+2*y[t]+5*t,y'[t]==3*x[t]+4*y[t]+17*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to t+\frac {1}{5} \left (2 (c_1-c_2) e^{2 t}+(3 c_1+2 c_2) e^{7 t}+5\right ) \\ y(t)\to -5 t-\frac {3}{5} (c_1-c_2) e^{2 t}+\frac {1}{5} (3 c_1+2 c_2) e^{7 t}-2 \\ \end{align*}