Internal problem ID [14022]
Internal file name [OUTPUT/13194_Friday_February_23_2024_06_58_41_AM_10307855/index.tex]
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.
ODE order: 1.
ODE degree: 1.
The type(s) of ODE detected by this program : "system of linear ODEs" Unable to solve or complete the solution.
Solve \begin {align*} x^{\prime }\left (t \right )&=\frac {15 y \left (t \right )}{t}-\frac {2 x \left (t \right )}{t}\\ y^{\prime }\left (t \right )&=\frac {x \left (t \right )}{t} \end {align*}
Does not currently support non autonomous system of first order linear differential equations. The following is the phase plot
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
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*x'[t]+2*x[t]==15*y[t],t*y'[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*}