Internal problem ID [12848]
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: 8.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=5 y_{1} \left (x \right )-5 y_{2} \left (x \right )-5 y_{3} \left (x \right )\\ y_{2}^{\prime }\left (x \right )&=-y_{1} \left (x \right )+4 y_{2} \left (x \right )+2 y_{3} \left (x \right )\\ y_{3}^{\prime }\left (x \right )&=3 y_{1} \left (x \right )-5 y_{2} \left (x \right )-3 y_{3} \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.109 (sec). Leaf size: 71
dsolve([diff(y__1(x),x)=5*y__1(x)-5*y__2(x)-5*y__3(x),diff(y__2(x),x)=-1*y__1(x)+4*y__2(x)+2*y__3(x),diff(y__3(x),x)=3*y__1(x)-5*y__2(x)-3*y__3(x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= {\mathrm e}^{2 x} \left (\sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{3} \right ) \\ y_{2} \left (x \right ) &= -\frac {\left (2 \sin \left (x \right ) c_{2} -\sin \left (x \right ) c_{3} +\cos \left (x \right ) c_{2} +2 \cos \left (x \right ) c_{3} -5 c_{1} \right ) {\mathrm e}^{2 x}}{5} \\ y_{3} \left (x \right ) &= {\mathrm e}^{2 x} \left (\sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{3} -c_{1} \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 109
DSolve[{y1'[x]==5*y1[x]-5*y2[x]-5*y3[x],y2'[x]==-1*y1[x]+4*y2[x]+2*y3[x],y3'[x]==3*y1[x]-5*y2[x]-3*y3[x]},{y1[x],y2[x],y3[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to e^{2 x} (c_1 \cos (x)+(3 c_1-5 (c_2+c_3)) \sin (x)) \\ \text {y2}(x)\to e^{2 x} (-c_1 (\sin (x)+\cos (x)-1)+c_3 (2 \sin (x)+\cos (x)-1)+c_2 (2 \sin (x)+\cos (x))) \\ \text {y3}(x)\to e^{2 x} (c_1 \cos (x)+(3 c_1-5 (c_2+c_3)) \sin (x)-c_1+c_3) \\ \end{align*}