Internal problem ID [12845]
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: 6 a.
ODE order: 1.
ODE degree: 1.
Solve \begin {align*} y_{1}^{\prime }\left (x \right )&=\frac {5 y_{1} \left (x \right )}{x}+\frac {4 y_{2} \left (x \right )}{x}\\ y_{2}^{\prime }\left (x \right )&=-\frac {6 y_{1} \left (x \right )}{x}-\frac {5 y_{2} \left (x \right )}{x} \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 34
dsolve([diff(y__1(x),x)=5/x*y__1(x)+4/x*y__2(x),diff(y__2(x),x)=-6/x*y__1(x)-5/x*y__2(x)],singsol=all)
\begin{align*} y_{1} \left (x \right ) &= \frac {c_{1} x^{2}+c_{2}}{x} \\ y_{2} \left (x \right ) &= -\frac {2 c_{1} x^{2}+3 c_{2}}{2 x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 34
DSolve[{y1'[x]==5/x*y1[x]+4/x*y2[x],y2'[x]==-6/x*y1[x]-5/x*y2[x]},{y1[x],y2[x]},x,IncludeSingularSolutions -> True]
\begin{align*} \text {y1}(x)\to \frac {c_1}{x}+c_2 x \\ \text {y2}(x)\to -\frac {3 c_1}{2 x}-c_2 x \\ \end{align*}