Internal problem ID [6290]
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 }\relax (t )&=2 x \relax (t )-y \relax (t )\\ y^{\prime }\relax (t )&=-x \relax (t )+2 y \relax (t )+4 \,{\mathrm e}^{t} \end {align*}
✓ Solution by Maple
Time used: 0.084 (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)],[x(t), y(t)], singsol=all)
\[ x \relax (t ) = -{\mathrm e}^{3 t} c_{2}+c_{1} {\mathrm e}^{t}+2 \,{\mathrm e}^{t} t +2 \,{\mathrm e}^{t} \] \[ y \relax (t ) = {\mathrm e}^{3 t} c_{2}+c_{1} {\mathrm e}^{t}+2 \,{\mathrm e}^{t} t \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 66
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-c_2) e^{2 t}+2+c_1+c_2\right ) \\ y(t)\to \frac {1}{2} e^t \left (4 t+(c_2-c_1) e^{2 t}-2+c_1+c_2\right ) \\ \end{align*}