Internal problem ID [5445]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 21. System of simultaneous linear equations. Supplemetary problems. Page
163
Problem number: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} x^{\prime }\left (t \right )&=3 x \left (t \right )-t^{2}+2 y \left (t \right )+t\\ y^{\prime }\left (t \right )&=t^{2}-3 y \left (t \right )-5 x \left (t \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve([diff(x(t),t)+2*x(t)+diff(y(t),t)+y(t)=t,5*x(t)+diff(y(t),t)+3*y(t)=t^2],[x(t), y(t)], singsol=all)
\begin{align*} x \left (t \right ) = -t^{2}-\frac {\cos \left (t \right ) c_{2}}{5}+\frac {\sin \left (t \right ) c_{1}}{5}+t +3-\frac {3 \sin \left (t \right ) c_{2}}{5}-\frac {3 \cos \left (t \right ) c_{1}}{5} y \left (t \right ) = \sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} +2 t^{2}-3 t -4 \end{align*}
✓ Solution by Mathematica
Time used: 0.122 (sec). Leaf size: 61
DSolve[{x'[t]+2*x[t]+y'[t]+y[t]==t,5*x[t]+y'[t]+3*y[t]==t^2},{x[t],y[t]},t,IncludeSingularSolutions -> True]
\begin{align*} x(t)\to -t^2+t+c_1 \cos (t)+(3 c_1+2 c_2) \sin (t)+3 y(t)\to 2 t^2-3 t+c_2 \cos (t)-(5 c_1+3 c_2) \sin (t)-4 \end{align*}