Internal problem ID [12849]
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: 9.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=4 y_{1} \left (x \right )+6 y_{2} \left (x \right )+6 y_{3} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=y_{1} \left (x \right )+3 y_{2} \left (x \right )+2 y_{3} \left (x \right )\\ y_{3}^{\prime }\left (x \right )&=-y_{1} \left (x \right )-4 y_{2} \left (x \right )-3 y_{3} \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 63
dsolve([diff(y__1(x),x)=4*y__1(x)+6*y__2(x)+6*y__3(x),diff(y__2(x),x)=1*y__1(x)+3*y__2(x)+2*y__3(x),diff(y__3(x),x)=-1*y__1(x)-4*y__2(x)-3*y__3(x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= c_{2} {\mathrm e}^{4 x}+c_{3} {\mathrm e}^{-x} \\ y_{2} \left (x \right ) &= \frac {c_{2} {\mathrm e}^{4 x}}{3}+\frac {c_{3} {\mathrm e}^{-x}}{3}+c_{1} {\mathrm e}^{x} \\ y_{3} \left (x \right ) &= -\frac {7 c_{3} {\mathrm e}^{-x}}{6}-\frac {c_{2} {\mathrm e}^{4 x}}{3}-c_{1} {\mathrm e}^{x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 145
DSolve[{y1'[x]==4*y1[x]+6*y2[x]+6*y3[x],y2'[x]==1*y1[x]+3*y2[x]+2*y3[x],y3'[x]==-1*y1[x]-4*y2[x]-3*y3[x]},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to \frac {1}{5} e^{-x} \left ((5 c_1+6 (c_2+c_3)) e^{5 x}-6 (c_2+c_3)\right ) \\ \text {y2}(x)\to \frac {1}{15} e^{-x} \left (-5 (c_1-3 c_2) e^{2 x}+(5 c_1+6 (c_2+c_3)) e^{5 x}-6 (c_2+c_3)\right ) \\ \text {y3}(x)\to \frac {1}{3} (c_1-3 c_2) e^x+\frac {7}{5} (c_2+c_3) e^{-x}-\frac {1}{15} (5 c_1+6 (c_2+c_3)) e^{4 x} \\ \end{align*}