Internal problem ID [5444]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 21. System of simultaneous linear equations. Supplemetary problems. Page
163
Problem number: 10.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=-x \left (t \right )+{\mathrm e}^{2 t}-{\mathrm e}^{t}\\ y^{\prime }\left (t \right )&=-x \left (t \right )+y \left (t \right )+{\mathrm e}^{2 t} \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 52
dsolve([diff(x(t),t)-diff(y(t),t)+y(t)=-exp(t),x(t)+diff(y(t),t)-y(t)=exp(2*t)],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = \frac {{\mathrm e}^{2 t}}{3}+2 \,{\mathrm e}^{-t} c_{2} -\frac {{\mathrm e}^{t}}{2} y \left (t \right ) = {\mathrm e}^{-t} c_{2} +c_{1} {\mathrm e}^{t}+\frac {2 \,{\mathrm e}^{2 t}}{3}+\frac {{\mathrm e}^{t} t}{2}-\frac {{\mathrm e}^{t}}{4} \end{align*}
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 72
DSolve[{x'[t]-y'[t]+y[t]==-Exp[t],x[t]+y'[t]-y[t]==Exp[2*t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{6} e^t \left (2 e^t-3\right )+c_1 e^{-t} y(t)\to \frac {2 e^{2 t}}{3}+\frac {c_1 e^{-t}}{2}+\frac {1}{4} e^t (2 t-1-2 c_1+4 c_2) \end{align*}