Internal problem ID [12850]
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: 10.
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 )-3 y_{3} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=-3 y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 y_{3} \left (x \right )\\ y_{3}^{\prime }\left (x \right )&=2 y_{1} \left (x \right )+y_{3} \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 102
dsolve([diff(y__1(x),x)=1*y__1(x)+2*y__2(x)-3*y__3(x),diff(y__2(x),x)=-3*y__1(x)+4*y__2(x)-2*y__3(x),diff(y__3(x),x)=2*y__1(x)+0*y__2(x)+1*y__3(x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= \frac {{\mathrm e}^{2 x} \left (3 \cos \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{3} +\sin \left (3 x \right ) c_{2} -3 \sin \left (3 x \right ) c_{3} +c_{1} \right )}{2} \\ y_{2} \left (x \right ) &= \frac {{\mathrm e}^{2 x} \left (6 \cos \left (3 x \right ) c_{2} -2 \cos \left (3 x \right ) c_{3} -2 \sin \left (3 x \right ) c_{2} -6 \sin \left (3 x \right ) c_{3} +7 c_{1} \right )}{4} \\ y_{3} \left (x \right ) &= {\mathrm e}^{2 x} \left (c_{1} +\sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{3} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 176
DSolve[{y1'[x]==1*y1[x]+2*y2[x]-3*y3[x],y2'[x]==-3*y1[x]+4*y2[x]-2*y3[x],y3'[x]==2*y1[x]+0*y2[x]+1*y3[x]},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to \frac {1}{9} e^{2 x} ((11 c_1-2 (c_2+c_3)) \cos (3 x)-3 (c_1-2 c_2+3 c_3) \sin (3 x)+2 (-c_1+c_2+c_3)) \\ \text {y2}(x)\to \frac {1}{9} e^{2 x} ((7 c_1+2 c_2-7 c_3) \cos (3 x)+(-9 c_1+6 c_2-6 c_3) \sin (3 x)+7 (-c_1+c_2+c_3)) \\ \text {y3}(x)\to \frac {1}{9} e^{2 x} ((4 c_1-4 c_2+5 c_3) \cos (3 x)+(6 c_1-3 c_3) \sin (3 x)+4 (-c_1+c_2+c_3)) \\ \end{align*}