Internal problem ID [12823]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 7. Systems of First-Order Differential Equations. Exercises page 329
Problem number: 4.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=y_{1} \left (x \right )+2 y_{2} \left (x \right )+x -1\\ y_{2}^{\prime }\left (x \right )&=3 y_{1} \left (x \right )+2 y_{2} \left (x \right )-5 x -2 \end {align*}
With initial conditions \[ [y_{1} \left (0\right ) = -2, y_{2} \left (0\right ) = 3] \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 18
dsolve([diff(y__1(x),x) = y__1(x)+2*y__2(x)+x-1, diff(y__2(x),x) = 3*y__1(x)+2*y__2(x)-5*x-2, y__1(0) = -2, y__2(0) = 3], singsol=all)
\begin{align*} y_{1} \left (x \right ) &= -2+3 x \\ y_{2} \left (x \right ) &= 3-2 x \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.316 (sec). Leaf size: 18
DSolve[{y1'[x]==y1[x]+2*y2[x]+x-1,y2'[x]==3*y1[x]+2*y2[x]-5*x-2},{y1[0]==-2,y2[0]==3},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to 3 x-2 \\ \text {y2}(x)\to 3-2 x \\ \end{align*}