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],singsol=all)
\begin{align*} x \left (t \right ) &= c_{2} \sin \left (t \right )+c_{1} \cos \left (t \right )-t^{2}+t +3 \\ y \left (t \right ) &= 2 t^{2}-\frac {3 c_{2} \sin \left (t \right )}{2}-\frac {3 c_{1} \cos \left (t \right )}{2}-3 t -4+\frac {c_{2} \cos \left (t \right )}{2}-\frac {c_{1} \sin \left (t \right )}{2} \\ \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*}