40.15.2 problem 11

Internal problem ID [6788]
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
Date solved : Monday, January 27, 2025 at 02:30:33 PM
CAS classification : system_of_ODEs

\begin{align*} \frac {d}{d t}x \left (t \right )+2 x \left (t \right )+\frac {d}{d t}y \left (t \right )+y \left (t \right )&=t\\ 5 x \left (t \right )+\frac {d}{d t}y \left (t \right )+3 y \left (t \right )&=t^{2} \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 53

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 )+\cos \left (t \right ) c_1 -t^{2}+t +3 \\ y \left (t \right ) &= 2 t^{2}+\frac {c_2 \cos \left (t \right )}{2}-\frac {\sin \left (t \right ) c_1}{2}-3 t -4-\frac {3 c_2 \sin \left (t \right )}{2}-\frac {3 \cos \left (t \right ) c_1}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.127 (sec). Leaf size: 61

DSolve[{D[x[t],t]+2*x[t]+D[y[t],t]+y[t]==t,5*x[t]+D[y[t],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*}