80.7.35 problem D 4

Internal problem ID [21354]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 7. System of first order equations. Excercise 7.6 at page 162
Problem number : D 4
Date solved : Sunday, October 12, 2025 at 05:51:27 AM
CAS classification : system_of_ODEs

\begin{align*} t^{2} \left (\frac {d}{d t}x \left (t \right )\right )-y \left (t \right )&=1\\ \frac {d}{d t}y \left (t \right )-2 x \left (t \right )&=0 \end{align*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 35

ode:=[t^2*diff(x(t),t)-y(t) = 1, diff(y(t),t)-2*x(t) = 0]; 
dsolve(ode);
 

\begin{align*} x \left (t \right ) &= \frac {c_2 \,t^{3}+c_1}{t^{2}} \\ y \left (t \right ) &= -1-\frac {-c_2 \,t^{3}+2 c_1}{t} \\ \end{align*}

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 34

ode={t^2*D[x[t],t]-y[t]==1,D[y[t],t]-2*x[t]==0}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {c_1}{t^2}+c_2 t\\ y(t)&\to c_2 t^2-\frac {2 c_1}{t}-1 \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(t**2*Derivative(x(t), t) - y(t) - 1,0),Eq(-2*x(t) + Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

NotImplementedError :