85.83.13 problem 4 (d)

Internal problem ID [23010]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 10. Systems of differential equations and their applications. A Exercises at page 444
Problem number : 4 (d)
Date solved : Thursday, October 02, 2025 at 09:17:29 PM
CAS classification : system_of_ODEs

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

✗ Maple

ode:=[x(t)*diff(y(t),t)+y(t)*diff(x(t),t) = t^2, 2*diff(diff(x(t),t),t)-diff(y(t),t) = 5*t]; 
dsolve(ode);
 

\[ \text {No solution found} \]

✗ Mathematica

ode={x[t]*D[y[t],{t,1}]+y[t]*D[x[t],t]==t^2,2*D[x[t],{t,2}]-D[y[t],t]==5*t}; 
ic={}; 
DSolve[{ode,ic},{x[t],y[t]},t,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
y = Function("y") 
ode=[Eq(-t**2 + x(t)*Derivative(y(t), t) + y(t)*Derivative(x(t), t),0),Eq(-5*t + 2*Derivative(x(t), (t, 2)) - Derivative(y(t), t),0)] 
ics = {} 
dsolve(ode,func=[x(t),y(t)],ics=ics)
 

ValueError : It solves only those systems of equations whose orders are equal