60.9.11 problem 1866

Internal problem ID [11865]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 8, system of first order odes
Problem number : 1866
Date solved : Monday, January 27, 2025 at 11:43:59 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+2 y \left (t \right )&=3 t\\ \frac {d}{d t}y \left (t \right )-2 x \left (t \right )&=4 \end{align*}

✓ Solution by Maple

Time used: 0.064 (sec). Leaf size: 38

dsolve({diff(x(t),t)+2*y(t)=3*t,diff(y(t),t)-2*x(t)=4},singsol=all)
 

\begin{align*} x \left (t \right ) &= \sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} -\frac {5}{4} \\ y \left (t \right ) &= -\cos \left (2 t \right ) c_{2} +\sin \left (2 t \right ) c_{1} +\frac {3 t}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.062 (sec). Leaf size: 156

DSolve[{D[x[t],t]+2*y[t]==3*t,D[y[t],t]-2*x[t]==4},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to \cos (2 t) \int _1^t(3 \cos (2 K[1]) K[1]+4 \sin (2 K[1]))dK[1]-\sin (2 t) \int _1^t(4 \cos (2 K[2])-3 K[2] \sin (2 K[2]))dK[2]+c_1 \cos (2 t)-c_2 \sin (2 t) \\ y(t)\to \cos (2 t) \int _1^t(4 \cos (2 K[2])-3 K[2] \sin (2 K[2]))dK[2]+\sin (2 t) \int _1^t(3 \cos (2 K[1]) K[1]+4 \sin (2 K[1]))dK[1]+c_2 \cos (2 t)+c_1 \sin (2 t) \\ \end{align*}