83.50.1 problem Ex 1 page 146

Internal problem ID [19639]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter IX. Simultaneous equations
Problem number : Ex 1 page 146
Date solved : Tuesday, January 28, 2025 at 02:05:56 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )-7 x \left (t \right )+y \left (t \right )&=0\\ \frac {d}{d t}y \left (t \right )-2 x \left (t \right )-5 y \left (t \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.049 (sec). Leaf size: 44

dsolve([diff(x(t),t)-7*x(t)+y(t)=0,diff(y(t),t)-2*x(t)-5*y(t)=0],singsol=all)
 

\begin{align*} x \left (t \right ) &= {\mathrm e}^{6 t} \left (\sin \left (t \right ) c_1 +\cos \left (t \right ) c_2 \right ) \\ y \left (t \right ) &= {\mathrm e}^{6 t} \left (\sin \left (t \right ) c_1 +\sin \left (t \right ) c_2 -\cos \left (t \right ) c_1 +\cos \left (t \right ) c_2 \right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 53

DSolve[{D[x[t],t]-7*x[t]+y[t]==0,D[y[t],t]-2*x[t]-5*y[t]==0},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to e^{6 t} (c_1 (\sin (t)+\cos (t))-c_2 \sin (t)) \\ y(t)\to e^{6 t} (c_2 \cos (t)+(2 c_1-c_2) \sin (t)) \\ \end{align*}