Internal problem ID [7044]
Book: Selected problems from homeworks from different courses
Section: Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale
college, Bloomington, Minnesota
Problem number: Example 8.3.4 from Handout chapter 8.2.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=6 x \left (t \right )-7 y \left (t \right )+10\\ y^{\prime }\left (t \right )&=x \left (t \right )-2 y \left (t \right )-2 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 45
dsolve([diff(x(t),t)=6*x(t)-7*y(t)+10,diff(y(t),t)=x(t)-2*y(t)-2*exp(t)],[x(t), y(t)], singsol=all)
\[ x \left (t \right ) = {\mathrm e}^{-t} c_{2} +7 c_{1} {\mathrm e}^{5 t}-\frac {7 \,{\mathrm e}^{t}}{4}-4 \] \[ y \left (t \right ) = {\mathrm e}^{-t} c_{2} +c_{1} {\mathrm e}^{5 t}-\frac {5 \,{\mathrm e}^{t}}{4}-2 \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 90
DSolve[{x'[t]==6*x[t]-7*y[t]+10,y'[t]==x[t]-2*y[t]-2*Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -\frac {7 e^t}{4}-\frac {1}{6} (c_1-7 c_2) e^{-t}+\frac {7}{6} (c_1-c_2) e^{5 t}-4 y(t)\to -\frac {5 e^t}{4}-\frac {1}{6} (c_1-7 c_2) e^{-t}+\frac {1}{6} (c_1-c_2) e^{5 t}-2 \end{align*}