Internal problem ID [12502]
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: 0.015 (sec). Leaf size: 47
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)],[y__1(x), y__2(x)], singsol=all)
\[ y_{1} \left (x \right ) = {\mathrm e}^{2 x} \left (\cos \left (x \right ) c_{1} -\cos \left (x \right ) c_{2} -\sin \left (x \right ) c_{1} -\sin \left (x \right ) c_{2} \right ) \] \[ y_{2} \left (x \right ) = {\mathrm e}^{2 x} \left (\cos \left (x \right ) c_{2} +\sin \left (x \right ) c_{1} \right ) \]
✓ 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*}