Internal problem ID [7043]
Book: Selected problems from homeworks from different courses
Section: Math 2520, summer 2021. Differential Equations and Linear Algebra. Normandale
college, Bloomington, Minnesota
Problem number: HW 5 problem 7.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=2 x \left (t \right )-y \left (t \right )\\ y^{\prime }\left (t \right )&=-x \left (t \right )+2 y \left (t \right )+4 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 45
dsolve([diff(x(t),t)=2*x(t)-y(t),diff(y(t),t)=-x(t)+2*y(t)+4*exp(t)],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} {\mathrm e}^{t}+c_{1} {\mathrm e}^{3 t}+2 \,{\mathrm e}^{t} t \\ y \left (t \right ) &= c_{2} {\mathrm e}^{t}-c_{1} {\mathrm e}^{3 t}+2 \,{\mathrm e}^{t} t -2 \,{\mathrm e}^{t} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 74
DSolve[{x'[t]==2*x[t]-y[t],y'[t]==-x[t]+2*y[t]+4*Exp[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} e^t \left (4 t+c_1 \left (e^{2 t}+1\right )-c_2 e^{2 t}+2+c_2\right ) \\ y(t)\to \frac {1}{2} e^t \left (4 t-c_1 e^{2 t}+c_2 e^{2 t}-2+c_1+c_2\right ) \\ \end{align*}