Internal problem ID [12844]
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: 5 c.
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 )+4 x -2\\ y_{2}^{\prime }\left (x \right )&=y_{1} \left (x \right )-2 y_{2} \left (x \right )+3 x \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 36
dsolve([diff(y__1(x),x)=2*y__1(x)-3*y__2(x)+4*x-2,diff(y__2(x),x)=y__1(x)-2*y__2(x)+3*x],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= c_{2} {\mathrm e}^{x}+{\mathrm e}^{-x} c_{1} +x \\ y_{2} \left (x \right ) &= \frac {c_{2} {\mathrm e}^{x}}{3}+{\mathrm e}^{-x} c_{1} -1+2 x \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.724 (sec). Leaf size: 101
DSolve[{y1'[x]==-2*y1[x]-3*y2[x]+4*x-2,y2'[x]==y1[x]-2*y2[x]+3*x},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to -\frac {x}{7}+c_1 e^{-2 x} \cos \left (\sqrt {3} x\right )-\sqrt {3} c_2 e^{-2 x} \sin \left (\sqrt {3} x\right )+\frac {4}{49} \\ \text {y2}(x)\to \frac {10 x}{7}+c_2 e^{-2 x} \cos \left (\sqrt {3} x\right )+\frac {c_1 e^{-2 x} \sin \left (\sqrt {3} x\right )}{\sqrt {3}}-\frac {33}{49} \\ \end{align*}