15.17.1 problem 1

Internal problem ID [3237]
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
Date solved : Monday, January 27, 2025 at 07:27:16 AM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )-x \left (t \right )&=\cos \left (t \right )\\ \frac {d}{d t}y \left (t \right )+y \left (t \right )&=4 t \end{align*}

✓ Solution by Maple

Time used: 0.065 (sec). Leaf size: 31

dsolve([diff(x(t),t)-x(t)=cos(t),diff(y(t),t)+y(t)=4*t],singsol=all)
 

\begin{align*} x \left (t \right ) &= -\frac {\cos \left (t \right )}{2}+\frac {\sin \left (t \right )}{2}+{\mathrm e}^{t} c_{1} \\ y \left (t \right ) &= 4 t -4+c_2 \,{\mathrm e}^{-t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 39

DSolve[{D[x[t],t]-x[t]==Cos[t],D[y[t],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*}