Internal problem ID [12532]
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: 12.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=y_{1} \left (x \right )+y_{2} \left (x \right )+2 y_{3} \left (x \right )\\ y_{3}^{\prime }\left (x \right )&=2 y_{1} \left (x \right )+2 y_{2} \left (x \right )+4 y_{3} \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 45
dsolve([diff(y__1(x),x)=1*y__1(x)+1*y__2(x)+2*y__3(x),diff(y__2(x),x)=1*y__1(x)+1*y__2(x)+2*y__3(x),diff(y__3(x),x)=2*y__1(x)+2*y__2(x)+4*y__3(x)],[y__1(x), y__2(x), y__3(x)], singsol=all)
\[ y_{1} \left (x \right ) = \frac {c_{3} {\mathrm e}^{6 x}}{2}-\frac {5 c_{2}}{2}-c_{1} \] \[ y_{2} \left (x \right ) = \frac {c_{2}}{2}+\frac {c_{3} {\mathrm e}^{6 x}}{2}+c_{1} \] \[ y_{3} \left (x \right ) = c_{2} +c_{3} {\mathrm e}^{6 x} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 114
DSolve[{y1'[x]==1*y1[x]+1*y2[x]+2*y3[x],y2'[x]==1*y1[x]+1*y2[x]+2*y3[x],y3'[x]==2*y1[x]+2*y2[x]+4*y3[x]},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to \frac {1}{6} \left (c_1 \left (e^{6 x}+5\right )+(c_2+2 c_3) \left (e^{6 x}-1\right )\right ) \text {y2}(x)\to \frac {1}{6} \left (c_1 \left (e^{6 x}-1\right )+c_2 \left (e^{6 x}+5\right )+2 c_3 \left (e^{6 x}-1\right )\right ) \text {y3}(x)\to \frac {1}{3} \left (c_1 \left (e^{6 x}-1\right )+c_2 \left (e^{6 x}-1\right )+c_3 \left (2 e^{6 x}+1\right )\right ) \end{align*}