Internal problem ID [12843]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 8. Linear Systems of First-Order Differential Equations. Exercises 8.3 page
379
Problem number: 5 a.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=2 y_{1} \left (x \right )-3 y_{2} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=y_{1} \left (x \right )-2 y_{2} \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 31
dsolve([diff(y__1(x),x)=2*y__1(x)-3*y__2(x),diff(y__2(x),x)=y__1(x)-2*y__2(x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x} \\ y_{2} \left (x \right ) &= \frac {c_{1} {\mathrm e}^{x}}{3}+c_{2} {\mathrm e}^{-x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 81
DSolve[{y1'[x]==-2*y1[x]-3*y2[x],y2'[x]==y1[x]-2*y2[x]},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to e^{-2 x} \left (c_1 \cos \left (\sqrt {3} x\right )-\sqrt {3} c_2 \sin \left (\sqrt {3} x\right )\right ) \\ \text {y2}(x)\to \frac {1}{3} e^{-2 x} \left (3 c_2 \cos \left (\sqrt {3} x\right )+\sqrt {3} c_1 \sin \left (\sqrt {3} x\right )\right ) \\ \end{align*}