73.27.3 problem 38.3

Internal problem ID [15688]
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 : Monday, March 31, 2025 at 01:45:08 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 )\\ t \left (\frac {d}{d t}y \left (t \right )\right )&=x \left (t \right ) \end{align*}

✓ Maple. Time used: 0.099 (sec). Leaf size: 33

ode:=[t*diff(x(t),t)+2*x(t) = 15*y(t), t*diff(y(t),t) = x(t)]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= -\frac {-3 c_2 \,t^{8}+5 c_1}{t^{5}} \\ y \left (t \right ) &= \frac {c_2 \,t^{8}+c_1}{t^{5}} \\ \end{align*}

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

ode={t*D[x[t],t]+2*x[t]==15*y[t],t*D[y[t],t]==x[t]}; 
ic={}; 
DSolve[{ode,ic},{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*}

✓ Sympy. Time used: 0.115 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(t*Derivative(x(t), t) + 2*x(t) - 15*y(t),0),Eq(t*Derivative(y(t), t) - x(t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

\[ \left [ x{\left (t \right )} = - \frac {5 C_{1}}{t^{5}} + 3 C_{2} t^{3}, \ y{\left (t \right )} = \frac {C_{1}}{t^{5}} + C_{2} t^{3}\right ] \]