10.11 problem 1923

Internal problem ID [10895]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 9, system of higher order odes
Problem number : 1923
Date solved : Friday, October 11, 2024 at 12:20:27 PM
CAS classification : system_of_ODEs

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

Does not currently support non autonomous system of first order linear differential equations.

10.11.1 Maple step by step solution

10.11.2 Maple dsolve solution

Solving time : 0.027 (sec)
Leaf size : 34

dsolve([(t^2+1)*diff(x(t),t) = -x(t)*t+y(t), (t^2+1)*diff(y(t),t) = -x(t)-t*y(t)] 
       ,{op([x(t), y(t)])})
 

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

10.11.3 Mathematica DSolve solution

Solving time : 0.008 (sec)
Leaf size : 39

DSolve[{{(t^2+1)*D[x[t],t]==-t*x[t]+y[t],(t^2+1)*D[y[t],t]==-x[t]-t*y[t]},{}}, 
       {x[t],y[t]},t,IncludeSingularSolutions->True]
 

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