Internal problem ID [12826]
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: 13 (a).
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=3 y_{1} \left (x \right )-2 y_{2} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=-y_{1} \left (x \right )+y_{2} \left (x \right ) \end {align*}
With initial conditions \[ [y_{1} \left (0\right ) = 1, y_{2} \left (0\right ) = -1] \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 119
dsolve([diff(y__1(x),x) = 3*y__1(x)-2*y__2(x), diff(y__2(x),x) = -y__1(x)+y__2(x), y__1(0) = 1, y__2(0) = -1], singsol=all)
\begin{align*} y_{1} \left (x \right ) &= \left (\frac {1}{2}+\frac {\sqrt {3}}{2}\right ) {\mathrm e}^{\left (2+\sqrt {3}\right ) x}+\left (\frac {1}{2}-\frac {\sqrt {3}}{2}\right ) {\mathrm e}^{-\left (-2+\sqrt {3}\right ) x} \\ y_{2} \left (x \right ) &= -\frac {\left (\frac {1}{2}+\frac {\sqrt {3}}{2}\right ) {\mathrm e}^{\left (2+\sqrt {3}\right ) x} \sqrt {3}}{2}+\frac {\left (\frac {1}{2}-\frac {\sqrt {3}}{2}\right ) {\mathrm e}^{-\left (-2+\sqrt {3}\right ) x} \sqrt {3}}{2}+\frac {\left (\frac {1}{2}+\frac {\sqrt {3}}{2}\right ) {\mathrm e}^{\left (2+\sqrt {3}\right ) x}}{2}+\frac {\left (\frac {1}{2}-\frac {\sqrt {3}}{2}\right ) {\mathrm e}^{-\left (-2+\sqrt {3}\right ) x}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 79
DSolve[{y1'[x]==3*y1[x]-2*y2[x],y2'[x]==-y1[x]+y2[x]},{y1[0]==1,y2[0]==-1},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to \frac {1}{2} e^{-\left (\left (\sqrt {3}-2\right ) x\right )} \left (\left (1+\sqrt {3}\right ) e^{2 \sqrt {3} x}+1-\sqrt {3}\right ) \\ \text {y2}(x)\to -\frac {1}{2} e^{-\left (\left (\sqrt {3}-2\right ) x\right )} \left (e^{2 \sqrt {3} x}+1\right ) \\ \end{align*}