Internal problem ID [12822]
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: 3.
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 )\\ y_{2}^{\prime }\left (x \right )&=y_{1} \left (x \right )+3 y_{2} \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 46
dsolve([diff(y__1(x),x)=y__1(x)-2*y__2(x),diff(y__2(x),x)=y__1(x)+3*y__2(x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= {\mathrm e}^{2 x} \left (\sin \left (x \right ) c_{1} +\cos \left (x \right ) c_{2} \right ) \\ y_{2} \left (x \right ) &= -\frac {{\mathrm e}^{2 x} \left (\sin \left (x \right ) c_{1} -\sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\cos \left (x \right ) c_{2} \right )}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 51
DSolve[{y1'[x]==y1[x]-2*y2[x],y2'[x]==y1[x]+3*y2[x]},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to e^{2 x} (c_1 \cos (x)-(c_1+2 c_2) \sin (x)) \\ \text {y2}(x)\to e^{2 x} (c_2 \cos (x)+(c_1+c_2) \sin (x)) \\ \end{align*}