Internal problem ID [12841]
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: 3.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=2 y_{2} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=3 y_{1} \left (x \right )\\ y_{3}^{\prime }\left (x \right )&=2 y_{3} \left (x \right )-y_{1} \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 107
dsolve([diff(y__1(x),x)=2*y__2(x),diff(y__2(x),x)=3*y__1(x),diff(y__3(x),x)=2*y__3(x)-y__1(x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= {\mathrm e}^{\sqrt {6}\, x} c_{2} +c_{3} {\mathrm e}^{-\sqrt {6}\, x} \\ y_{2} \left (x \right ) &= \frac {\sqrt {6}\, \left ({\mathrm e}^{\sqrt {6}\, x} c_{2} -c_{3} {\mathrm e}^{-\sqrt {6}\, x}\right )}{2} \\ y_{3} \left (x \right ) &= \frac {2 \,{\mathrm e}^{2 x} c_{1}}{\left (2+\sqrt {6}\right ) \left (-2+\sqrt {6}\right )}+\frac {{\mathrm e}^{-\sqrt {6}\, x} c_{3}}{2+\sqrt {6}}-\frac {{\mathrm e}^{\sqrt {6}\, x} c_{2}}{-2+\sqrt {6}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 232
DSolve[{y1'[x]==2*y2[x],y2'[x]==3*y1[x],y3'[x]==2*y3[x]-y1[x]},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to \frac {1}{6} e^{-\sqrt {6} x} \left (3 c_1 \left (e^{2 \sqrt {6} x}+1\right )+\sqrt {6} c_2 \left (e^{2 \sqrt {6} x}-1\right )\right ) \\ \text {y2}(x)\to \frac {1}{4} e^{-\sqrt {6} x} \left (\sqrt {6} c_1 \left (e^{2 \sqrt {6} x}-1\right )+2 c_2 \left (e^{2 \sqrt {6} x}+1\right )\right ) \\ \text {y3}(x)\to \frac {1}{12} e^{-\sqrt {6} x} \left (2 \left (c_2 \left (-\left (3+\sqrt {6}\right ) e^{2 \sqrt {6} x}+6 e^{\left (2+\sqrt {6}\right ) x}-3+\sqrt {6}\right )+6 c_3 e^{\left (2+\sqrt {6}\right ) x}\right )-3 c_1 \left (\left (2+\sqrt {6}\right ) e^{2 \sqrt {6} x}-4 e^{\left (2+\sqrt {6}\right ) x}+2-\sqrt {6}\right )\right ) \\ \end{align*}