Internal problem ID [2266]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 26, page 115
Problem number: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=x \left (t \right )+\cos \left (t \right )\\ y^{\prime }\left (t \right )&=-y \left (t \right )+4 t \end {align*}
✓ Solution by Maple
Time used: 0.234 (sec). Leaf size: 32
dsolve([diff(x(t),t)-x(t)=cos(t),diff(y(t),t)+y(t)=4*t],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = -\frac {\cos \left (t \right )}{2}+\frac {\sin \left (t \right )}{2}+c_{1} {\mathrm e}^{t} y \left (t \right ) = 4 t -4+c_{2} {\mathrm e}^{-t} \end{align*}
✓ Solution by Mathematica
Time used: 0.076 (sec). Leaf size: 39
DSolve[{x'[t]-x[t]==Cos[t],y'[t]+y[t]==4*t},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to \frac {1}{2} \left (\sin (t)-\cos (t)+2 c_1 e^t\right ) y(t)\to 4 t+c_2 e^{-t}-4 \end{align*}