Internal problem ID [12839]
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: 1.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=2 y_{1} \left (x \right )-3 y_{2} \left (x \right )+5 \,{\mathrm e}^{x}\\ y_{2}^{\prime }\left (x \right )&=y_{1} \left (x \right )+4 y_{2} \left (x \right )-2 \,{\mathrm e}^{-x} \end {align*}
✓ Solution by Maple
Time used: 0.157 (sec). Leaf size: 112
dsolve([diff(y__1(x),x)=2*y__1(x)-3*y__2(x)+5*exp(x),diff(y__2(x),x)=y__1(x)+4*y__2(x)-2*exp(-x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= {\mathrm e}^{3 x} \cos \left (\sqrt {2}\, x \right ) c_{2} +{\mathrm e}^{3 x} \sin \left (\sqrt {2}\, x \right ) c_{1} +\frac {{\mathrm e}^{-x}}{3}-\frac {5 \,{\mathrm e}^{x}}{2} \\ y_{2} \left (x \right ) &= -\frac {{\mathrm e}^{3 x} \cos \left (\sqrt {2}\, x \right ) c_{2}}{3}+\frac {{\mathrm e}^{3 x} \sqrt {2}\, \sin \left (\sqrt {2}\, x \right ) c_{2}}{3}-\frac {{\mathrm e}^{3 x} \sin \left (\sqrt {2}\, x \right ) c_{1}}{3}-\frac {{\mathrm e}^{3 x} \sqrt {2}\, \cos \left (\sqrt {2}\, x \right ) c_{1}}{3}+\frac {{\mathrm e}^{-x}}{3}+\frac {5 \,{\mathrm e}^{x}}{6} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 108
DSolve[{y1'[x]==2*y1[x]-3*y2[x]+5*Exp[x],y2'[x]==y1[x]+4*y2[x]-2*Exp[-x]},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to -\frac {1}{2} e^x \left (-2 c_1 e^{2 x} \cos \left (\sqrt {2} x\right )+\sqrt {2} (c_1+3 c_2) e^{2 x} \sin \left (\sqrt {2} x\right )+5\right ) \\ \text {y2}(x)\to \frac {5 e^x}{6}+c_2 e^{3 x} \cos \left (\sqrt {2} x\right )+\frac {(c_1+c_2) e^{3 x} \sin \left (\sqrt {2} x\right )}{\sqrt {2}} \\ \end{align*}