83.42.1 problem 13

Internal problem ID [19508]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter IX. Simultaneous equations. Excercise IX (A) at page 154
Problem number : 13
Date solved : Tuesday, January 28, 2025 at 08:32:49 PM
CAS classification : system_of_ODEs

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

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 30

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

\begin{align*} x &= \frac {c_{2} t^{2}+c_{1}}{t} \\ y &= \frac {-c_{2} t^{2}+c_{1}}{t} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.002 (sec). Leaf size: 31

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

\begin{align*} x(t)\to c_1 t+\frac {c_2}{t} \\ y(t)\to \frac {c_2}{t}-c_1 t \\ \end{align*}