73.27.3 problem 38.3

Internal problem ID [15759]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 38. Systems of differential equations. A starting point. Additional Exercises. page 786
Problem number : 38.3
Date solved : Tuesday, January 28, 2025 at 08:25:34 PM
CAS classification : system_of_ODEs

\begin{align*} t \left (\frac {d}{d t}x \left (t \right )\right )+2 x \left (t \right )&=15 y \left (t \right )\\ \left (\frac {d}{d t}y \left (t \right )\right ) t&=x \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.043 (sec). Leaf size: 32

dsolve([t*diff(x(t),t)+2*x(t)=15*y(t),t*diff(y(t),t)=x(t)],singsol=all)
 

\begin{align*} x \left (t \right ) &= \frac {3 c_{1} t^{8}-5 c_{2}}{t^{5}} \\ y \left (t \right ) &= \frac {c_{1} t^{8}+c_{2}}{t^{5}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 36

DSolve[{t*D[x[t],t]+2*x[t]==15*y[t],t*D[y[t],t]==x[t]},{x[t],y[t]},t,IncludeSingularSolutions -> True]
 

\begin{align*} x(t)\to 3 c_2 t^3-\frac {5 c_1}{t^5} \\ y(t)\to \frac {c_2 t^8+c_1}{t^5} \\ \end{align*}