Internal problem ID [12851]
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: 11.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=-2 y_{1} \left (x \right )-y_{2} \left (x \right )+y_{3} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=-y_{1} \left (x \right )-2 y_{2} \left (x \right )-y_{3} \left (x \right )\\ y_{3}^{\prime }\left (x \right )&=y_{1} \left (x \right )-y_{2} \left (x \right )-2 y_{3} \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 51
dsolve([diff(y__1(x),x)=-2*y__1(x)-1*y__2(x)+1*y__3(x),diff(y__2(x),x)=-1*y__1(x)-2*y__2(x)-1*y__3(x),diff(y__3(x),x)=1*y__1(x)-1*y__2(x)-2*y__3(x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= c_{2} +c_{3} {\mathrm e}^{-3 x} \\ y_{2} \left (x \right ) &= -c_{2} -c_{3} {\mathrm e}^{-3 x}+c_{1} {\mathrm e}^{-3 x} \\ y_{3} \left (x \right ) &= -2 c_{3} {\mathrm e}^{-3 x}+c_{2} +c_{1} {\mathrm e}^{-3 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 130
DSolve[{y1'[x]==-2*y1[x]-1*y2[x]+1*y3[x],y2'[x]==-1*y1[x]-2*y2[x]-1*y3[x],y3'[x]==1*y1[x]-1*y2[x]-2*y3[x]},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to \frac {1}{3} e^{-3 x} \left (c_1 \left (e^{3 x}+2\right )-(c_2-c_3) \left (e^{3 x}-1\right )\right ) \\ \text {y2}(x)\to \frac {1}{3} e^{-3 x} \left (-\left (c_1 \left (e^{3 x}-1\right )\right )+c_2 \left (e^{3 x}+2\right )-c_3 \left (e^{3 x}-1\right )\right ) \\ \text {y3}(x)\to \frac {1}{3} e^{-3 x} \left (c_1 \left (e^{3 x}-1\right )-c_2 \left (e^{3 x}-1\right )+c_3 \left (e^{3 x}+2\right )\right ) \\ \end{align*}